If `y=m_1x+c` and `y=m_2x+c` are two tangents to the parabola `y^2+4a(x+a)=0` , then

If y+3=m_1(x+2) and y+3=m_2(x+2) are two tangents to the parabola y^2=8x , then

If y=2x-3 is tangent to the parabola y^2=4a(x-1/3), then a is equal to

y=x is tangent to the parabola y=ax^(2)+c . If a=2, then the value of c is

The line 4x+2y = c is a tangent to the parabola y^(2) = 16x then c is :

The line y = mx + 1 is a tangent to the parabola y^(2) = 4x if m = _____

y^(2)=4xandy^(2)=-8(x-a) intersect at points A and C. Points O(0,0), A,B (a,0), and c are concyclic. Tangents to the parabola y^(2)=4x at A and C intersect at point D and tangents to the parabola y^(2)=-8(x-a) intersect at point E. Then the area of quadrilateral DAEC is

y=x is tangent to the parabola y=ax^(2)+c . If c=2, then the point of contact is

If y = 2x + c is a tangent to the circel x^(2) + y^(2) = 5 , then c is

A point P moves such that the chord of contact of the pair of tangents from P on the parabola y^2=4a x touches the rectangular hyperbola x^2-y^2=c^2dot Show that the locus of P is the ellipse (x^2)/(c^2)+(y^2)/((2a)^2)=1.

Two straight lines (y-b)=m_1(x+a) and (y-b)=m_2(x+a) are the tangents of y^2=4a x. Prove m_1m_2=-1.