Find the length and ends of the LR of `y^2-2x-8y-23=0`

Find the length and ends of the LR of x^2+8y-16x+24=0

Answer the following:Find the equations of the tangents to the circle x^2+y^2-2x+8y-23=0 having slope 3.

The length of latus rectum of the paraboal x^2-4x-8y+12=0 is ______.

The vertex of the parabola x^2-4x-8y-20=0 , is

Find the centre and radius of each of the following: x^2+y^2-6x-8y-24=0

Find the centre and radius of each of the following: 2x^2+2y^2+3x+4y+9/8=0

Let the line segment joining the centres of the circles x^(2)-2x+y^(2)=0 and x^(2)+y^(2)+4x+8y+16=0 intersect the circles at P and Q respectively. Then the equation of the circle with PQ as its diameter is

Let the line segment joining the centres of the circles x^2-2x+y^2=0 and x^2+y^2+4x+8y+16=0 intersect the another circle at P and Q respectively. Then the equation of the circle with PQ as its diameter is

The parabola x^2=4ay passes through (-2,1) Find the co-ordinates ends of the LR and equation of thr directrix.

Find the equation of the tangent to the parabola y^(2) = 8x which is parallel to the line 2x + 2y + 5 = 0 . Find its point of contact.