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.

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.

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

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

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.

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 =0

find the equation of the circle with this chord as diameter

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.

ams is 50root (3/13) plzz explain

3. 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 is

a) x=0 b)x+1=0 c)y=0 d) none of these

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 ) ?

the 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

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.^{2}+y^{2}=25an 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.${x}^{2}+{y}^{2}$— 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 ?

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.

^{n}of the Director - circle of the conic $\frac{l}{r}=1+e\mathrm{cos}\theta $find the eq^{n}to the locus of the foot of the perpendicular form the focus of the above conic on the tangent.the line lx + my +n=0 is a normal to the parabola y^2 = 4ax if

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

^{2}+y^{2}+z^{2}+2ux+2vy+2wz = 0find the locus of the mid point of the portion of the line x cosa +yp sin a = p which is intercepted between the axis ??

^{2}+ by^{2}+ cz^{2}= 1.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?

^{2},2at) on the parabola y^{2}=4ax, two normals can be drawn and their feet Q and R have the parameters satisfying the equation &^{2 }+ &t+2=0Prove 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

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.

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.1)touches y axis at (0,?3) and passes through (-1,0)

2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1)

3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0.

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

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 ) ?the 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