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Syllabus

Find the equation of the common tangent of parabola y

^{2}=4ax and x^{2}=4by.Show that the semi latus rectum of the parabola y

^{2}= 4ax is a harmonic mean between the segment of any focal chord.## The equation of the hyperbola whose directrix is x+2y=1,focus (2,1) and eccentricity 2 will be?

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.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.

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.

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.

find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4 and x + 2y = 5

In case of parabola

y= x

^{2}-2x-3Find:

a)Vertex:

b)Axis:

c)Focus:

d)Directrix:

e)Latus Rectum:

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

^{2}/a^{2}+ y^{2}/b^{2}= 1.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.

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 .

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

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

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

an ellipse whose foci are(2,4 and (14,9) and touches x)-axis ,then its eccentricity is ?

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.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

^{2}=4ax,the locus of middle points of all chords of constant length c isone 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

Find the equation for the ellipse that satisfies the given conditions: Major axis on the

x-axis and passes through the points (4, 3) and (6, 2).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

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}+ y^{2}= 100 that passes through (1,7) and subtends an angle of 120 at the origin is what?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}=6IfPis 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}A)vertex is (2a/3,0) , (7,0)

B)directrix is x=0

C)latus rectum is 2a/3

D)focus is (a,0)

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.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)

find the equation of ellipse .the distance between foci is 8 unit and the distance between directrix is 18 units.

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

(a)40,10

(b)40,-10

(c)-40,10

(d)-40,-10

how can we derive standard equation of ellipse

^{2}=32x ; then the other end of the chord isThe 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.Find the equation of parabola :

vertex =(2,1)

directrix : x = y-1

Find the coordinate of the point of intersection of the axis and the directrix of the parabola whose focus is (3,3) and the directrix is 3x-4y=2 . find also the latus rectum.

(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

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) isQFind the equation of the hyperbola with centre as the origin, transverse axis along x - axis, ecentricity √5 and the sum of whose semi - axes is 9.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

Find the vertex, axis, focus, directrix, tangent at the vertex, and length of the latus rectum of the parabola:

2y

^{2 }+ 3y - 4x - 3 = 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) .^{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 ?^{2}+y^{2}-4x=0 which is bisected at the point (1,1).{Please mention the requires formula in details)

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}=4 orthogonally and having its centre on the line 2x-2y+9=0,passes through two fixed points. Those points are?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.

Show that the circle x^2+y^2-2ax-2ay+a^2=0 touches both the coordinate axes.

If P is any point on hyperbola whose axis are equal,prove that SP.S'P=CP

^{2 }?the straight line kx+y=4 touches the parabola y=x-x^2, if k=?

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