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Syllabus

Find the equation of the common tangent of parabola y

^{2}=4ax and x^{2}=4by.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.

Show that the semi latus rectum of the parabola y

^{2}= 4ax is a harmonic mean between the segment of any focal chord.find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5

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.^{2}+y^{2}=4 orthogonally and having its centre on the line 2x-2y+9=0,passes through two fixed points. Those points are?Find the equations of circle passing through the points (1,1),(2,2) and whose radius is 1 units?

the line lx + my +n=0 is a normal to the parabola y^2 = 4ax if

x^{2}+y^{2}= 25 intercepts chords of length 8 units have equations(a) $2x+3y=13,x+5y=17$

(b) $y=3,12x+5y=39$

(c) $x=2,9x-11y=51$

(d) none of these

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 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.

^{2}/a^{2}+ y^{2}/b^{2}= 1.Prove that (-1,6), (5,2), (7,0), and (-1,-4) are concyclic.

Find the standard equation of ellipse whose focus is (1,0), the directrix is x+y+1=0 and eccentricity is 1/root2

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}=6The 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.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 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

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)=0one 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.

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

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 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

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

^{2}/a^{2 }+y^{2}/b^{2}is b^{2}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.^{2}+2y^{2}=1 subtends a right angle at the centre of the ellipse isFind 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}+y^{2}-4x=0 which is bisected at the point (1,1).{Please mention the requires formula in details)

how can we derive standard equation of ellipse

find the points of intersection of the line x-y+2=0 and the circle 3Xsquare + 3Ysquare -29x -19y +56 =0. also find the length of the chord intersepted.

on the ellipse whose foci are (-1,0) and (7,0) and eccentricity 1/2 is

A 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)

^{2}+y^{2}= 16 at the points where it is met by the circle x^{2}+y^{2}-5x+3y-2=0, the point of intersection of these tangetnts is ?Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

^{2}= 4ax which pass through the point (-6a,0) and which subtends an angle of 45$\xb0$ at the vertex.(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

if a tangent to an ellipse x

^{2}/a^{2}+y^{2}/b^{2}=1 with slope m is a normal to the circle x^{2}+y^{2}+4x+1=0, then maximum value of ab isthe 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

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}+2y^{2}=2,then the locus of the mid point of the intercept made by the tangents between the coordinate axis isA 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 isA 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.

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

^{2 }+ y^{2}= 6 and x^{2 }+ y^{2 }- 6x – 8 = 0 are given. The equation of circle through their points of intersection and the point (1,1) 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) is^{2}+30x+2y+59=0what is co-axial circle how to determine its equation and also tell its figure

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

^{1/2}x + 3 = 0 cuts the parabola y^{2}= x + 2 at A and B, and if P = (3^{1/2}, 0), then PA.PB is equal to?find the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

the minimum area of triangle formed by tangents to ellipse x

^{2}/a^{2}+y^{2}/b^{2}=1 and the coordinate axes isabasquare+bsquare)/2a+b)square/2asquare+ab+bsquare)/3In 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 ) ?If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP

^{2 }?Show that the 4 points (0,0),(1,1),(5,-5) and (6,-4) are concyclic.Please answer it fast , very urgent!!!!!!