Let A and B be two distinct points on the parabola y2=4x. If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be
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If PSQ is a focal chord of the ellipse 16x2+25y2=400 such that SP=8, then find the length of SQ. is (a) 21 (b) 94 (c) 98 (d) 916
Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the rectum for y2=12x
Find the equation of the parabola that satisfies the following conditions: Focus (0,−3); directrix y=3
A point P
moves such that the chord of contact of the pair of tangents from P
on the parabola y2=4ax
touches the rectangular hyperbola x2−y2=c2˙
Show that the locus of P
is the ellipse c2x2+(2a)2y2=1.
An arch is in the form of a parabola with its axis vertical. The arch is 10 m high and 5 m wide at the base. How wide is it 2 m form the vertex of the parabola?
Find the equation of the parabola that satisfies the following conditions: Vertex (0,0) passing through (5,2) and symmetric with respect to y- axis
If the normal at one end of the latus rectum of the ellipse a2x2+b2y2=1 passes through one end of the minor axis, then prove that eccentricity is constant.
Find the centre and radius of the circle 2x2+2y2−x=0