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Find the equation of the common tangent of parabola y

^{2}=4ax and x^{2}=4by.^{2 }+ y^{2}+ 2b_{1}y + 1 = 0 and x^{2}+ y^{2}+ 2b_{2}y + 1 = 0 cuts orthogonally, then the value of b_{1}b_{2}is?Show that the semi latus rectum of the parabola y

^{2}= 4ax is a harmonic mean between the segment of any focal chord.an equilateral triangle is inscribed in the parabola y

^{2}=4ax,where one vertex is at the vertex of the parabola.find the length of the side of the triangle.pls answer me as soon as possible.The focus of parabola is (1,5) and its directrix is x + y + 2 = 0. Find the equation of the parabola, its vertex and length of latus rectum.

^{2}+y^{2}+z^{2}+2ux+2vy+2wz = 0the line lx + my +n=0 is a normal to the parabola y^2 = 4ax if

^{2}+2y -3x +5 =0.find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5

^{2}/ 4 ) + ( y^{2}/9 ) .find the locus of the mid point of the portion of the line x cosa +yp sin a = p which is intercepted between the axis ??

Find the equation of the hyperbola having its foci at (0,root14) and (0,-root14) and passing through the point P(3,4)...

Find the equation of the circle which has its centre at the point (3,4) and touches the straight the line 5x+12y-1=0.

Find the equqtion of the circle which touches the axes and whose centre lies on x-2y=3.

A circle whose centre is the point of the intersection of the lines 2x-3y+4=0 and 3x+4y-5=0 passes through the origin. find its equation.

A circle of radius 4 units touches the coordinate axes in the first quadrant. Find the equation of its images with respect to the line mirrors x=0 and y=0.

One diameter of the circle circumscribing the rectangle ABCD is 4y=x+7. If the coordinates of A and B are (-3,4) and (5,4) respectively. Find its equation.

Find the equations of circle passing through the points (1,1),(2,2) and whose radius is 1 units?

FIND THE LENGTH OF THE CHORD INTERCEPTED BY THE CIRCLE x2+y2-x+3y-22 ON THE LINE y=x-3

Prove that (-1,6), (5,2), (7,0), and (-1,-4) are concyclic.

^{2}/a^{2 }+y^{2}/b^{2}is b^{2}e

if y = 2x is a chord of the circle x

^{2}+ y^{2}- 10x =0find the equation of the circle with this chord as diameter

The centre of a circle passing through the points (0,0) & (1,0) & touching the circle x2+y2=9 is: ans is (1/2 , +-root2)..explainAB is a chord of circle x2+y2=25 . The tangents of A & B intersect at C. If (2,3) is the mid-point of AB , the area of quadrilateral OACB is:ams is 50root (3/13) plzz explain3. Extremities of a dagonal of a rectangle are (0,0) & (4,3).Find the equations of the tangents to the circumcentre ofthe reactangle which are parallel to this diagonal.4. Find the equ. of circle described on the common cord of the circles x2+y2-4x-5=0 & x2+y2+8y+7=0 as diameter.ans is x2+y2-2x+4y+1=0..explain.^{2}+y^{2}=1, x^{2}+y^{2}-8x+15=0,x^{2}+y^{2}+10 y+24=0 .the point from which tangents of equal length can be drawn to all these three circles is____The parametric equations of a parabola are x=t

^{2}+1, y=2t+1.The cartesian equation of its directrix isa) x=0 b)x+1=0 c)y=0 d) none of these

find the equation of the circle passing through origin and cutting off intercepts a and b from x axis and y axis

one diameter of the circle circumscribing the rectangle ABCD is 4y=x+7.If the coordinates of A & B are (-3,4) &(5,4) respectively , find the equation of the circle.

^{2}+ y^{2}= 100 that passes through (1,7) and subtends an angle of 120 at the origin is what?Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

A circle of constant radius 'a' passes through origin 'O' and cuts the coordinate axes in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is

(a) (x^2+y^2)(1/x^2+1/y^2)=4a^2

(b) (x^2+y^2)(1/x^2+1/y^2)=a^2

(c) (x^2+y^2)^2(1/x^2+1/y^2)=4a^2

(d) (x^2+y^2)(1/x^2+1/y^2)=a^2

Find the equation of the circle which passes through the focus of the parabola x2 = 4y touches it at the point (6,9).

a tangent to the ellipse x

^{2}+ 4y^{2}=4 meets the ellipse x^{2}+2y^{2}=6 at P and Q.the angle between the tangents at P and Q of the ellipse x^{2}+2y^{2}=61)

if parabola y^{2}=px passes through point (2,-3),find the length of latus rectum .2) find the value of p so that the equation x^{2}+y^{2}- 2px+ 4y - 12=0 may represent a circle of radius 5 units .3) one end of the diameter of a circle x2+y2-6x+5y-7=0 os (7,-8).find the co-ordinates of other end

if the line 2x - y +1 = 0 touches the circle at the point (2,5) and the center of the circle lies on the line x+y -9 =0 find the eqn of circle

Q Read the following write up carefully and answer the following questions:Q. Let ABC be triangle whose equation of sides are AB $\equiv $ x + 2y = 3, AC $\equiv $2x + y = 3 and BC$\equiv $x + y = 4. S

_{l}, S_{2}, S_{3}are three circles drawn considering AB, AC and BC as diameter respectively. The radical axis of S_{1}and S_{2}, S_{l}and S_{3}and S_{2}and S_{3}are L_{12}= O, L_{13}= O, L_{23}= O. These radical axes meet sides BC, AC and AB at D, E and F respectively and triangle DEF is formed.Q. 1. Equation to circumcircle of triangle ADC is(A) x

^{2}+y^{2}-6x+4=0 (B) x^{2}+y^{2}-6y+4=0(C) x

^{2}+y^{2}+6x+4=0 (D) None of these.the tangent to curv y= x^2 + 6 at a point 1,7 touches the circle x^2+y^2+16x+12y+c=0 at a point q then the coordinates of q are :

ans = -6,-7

Find the equation of the circle passing through the points (4, 1) and (6, 5) and whose centre is on the line 4

x+y= 16.^{2}+2y^{2}=1 subtends a right angle at the centre of the ellipse isA tangent to the ellipse 4x2+9y2=36 is cut by the tangent at the extremities of the major axis at T and T'. The circle on TT' as diameter passes through the point

(A) (0-$\sqrt{}$5) (B) ( $\sqrt{}$ 5, 0 )

(C) (0,0) (D) (3,2)

IfPis a point on the hyperbola 16 x^{2}- 9y^{2}=144 whose foci are s_{1}and s_{2}, then Find PS_{1}- PS_{2}The foci of a hyperbola coincide with the foci of the ellipse x2/25 + y2/9=1.Find the equation of the hyperbola,if its eccentricity is 2.

^{2 }+ 5y^{2 }= 20 bisected at the point (2,1) is :a). 4x + 5y + 13 = 0

b). 4x + 5y = 13

c). 5x+4y+13 = 0

d). 5x+4y = 13

The equations of the tangents drawn from the origin to the circle x

^{2}+ y^{2}- 2rx- 2hy + h^{2}=0 are :^{2}-r^{2})x-2rhy=0, x=0^{2}-r^{2})x + 2rhy=0,x=0.how can we derive standard equation of ellipse

if the chord of contact of tangents from a point P(h,k) to the circle x^{2}+ y^{2}= a^{2}touches the circle x^{2}+ (y-a)^{2}= a^{2}, then locus of P isFind the equation of parabola :

vertex =(2,1)

directrix : x = y-1

^{2}/a^{2}+ y^{2}/b^{2}= 1.(A) straight line parallel to x-axis (B) straight line parallel to y-axis

(C) circle of radius sq.rt.2 (D) circle of radius sq.rt.3

Q.41. Let P be a point on the circle ${x}^{2}+{y}^{2}=9$, Q a point on the line 7x + y + 3 = 0, and the perpendicular bisector of PQ be the line x - y + 1 = 0. Then, the coordinates of P are

(a) (3, 0)

(b) (0, 3)

(c) (72 / 25, - 21 / 25)

(d) (- 72 / 25, - 21 / 25)

Please do this question both by Maxima and minima and simple method . Please please please do it by both the methods . Do not forget to do it by both the methods .

A man running a race course notes that the sum of the distances from the two flag posts from him is always 10m and the distance between the flag posts is 8 metres. Find the equation of the path traced by the man.

If P(-3,2) is one end of the focal chord PQ of the parabolay^2+4x+4y=0, then the slope of the normal at Q isthe angle subtended by common tangents of two ellipses 4(x-4)

^{2 }+25y^{2}=100 4(x+1)^{2}+ y^{2}=4 at the origin (in degrees) isfind the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

In case of parabola

y= x

^{2}-2x-3Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum:

find the equation of circle whose centre is the point of intersection of the lines 2x-3y+4=0 and 3x+4y-5=0 passes through the origin.

find the equation of circle which passes through the centre of the circle x

^{2}+y^{2}-4x-8y-41=0 and is concentric with x^{2}+y^{2}-2y+1=0prove tht points (2,-4)(3,-1)(3,-3)(0, 0)are concyclic

answer fast.urgent

what is co-axial circle how to determine its equation and also tell its figure

Show that the circle on the chord xcosα + ysinα - p = 0 of the circle x

^{2}+y^{2}= a^{2}as diameter is x^{2}+ y^{2}- a^{2}-2p(xcosα +ysinα -p)=0^{2}+y^{2}-4x=0 which is bisected at the point (1,1).{Please mention the requires formula in details)

Find the distance between the chords of contact of the tangent to the circle x

^{2 }+y^{2 }+2gx+2fy+c=0 from the origin and the point (g,f) .In an ellipse, x

^{2}/a^{2}+ y^{2}/b^{2}= 1, a>b, if the focal distances of a point on the ellipse ( the point is neither on X-axis nor on Y-axis ) are r_{1}and r_{2}, then find the length of the normal drawn at this point ( length of normal means the length of the portion of the normal between the point and the major axis ) ?1. the ecentricity of an ellipse is 1/2, focus is S(0,0) and the major axis and directrix intersect at Z(-1,-1). find the coordinates of the center of the ellipse.

2. show that the sum of the focal distances of any point on the ellipse 9x

^{2}+16y^{2 }=144 is constant.3.A point moves on a plane in such a manner that the sum of its distances from the points (5,0) and (-5,0) is always constant and equal to 26. show that the locus of the moving point is the ellipse x

^{2}/169+y^{2 }/144=1.4. show that for an ellipse the straight line joining the upper end of one of the latus rectum and the lower end of other latus rectum passes through the center of the ellipse.

A circle of radius 2 lies in the first quadrant and touches both the axis.Find the equation of the circle with the centre at (6,5) and touching the above circle externally.

^{2}+y^{2 }=a^{2}.

^{2}+ by^{2}+ cz^{2}= 1.If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP

^{2 }?${x}^{2}+{y}^{2}$— 16 = 0 and ${x}^{2}+{y}^{2}$ — 8x — 12y + 16 = 0.

If tangents are drawn from the centre of the variable circles to S. Then the locus of the mid point of the chord of contact of these tangents will be ?

Find the equation of the circle with radius 5 whose centre lies on x-axis & passes through the point (2,3)?

Find the equation of a parabola whose end points of Latus rectum are given by (7,5) and (7,3). also find the end points where this parabola meets the coordinate axes?