Let P be the point on parabola y2=4x which is at the shortest distance from the center S of the circle x2+y2−4x−16y+64=0 let Q be the point on the circle dividing the line segment SP internally. Then
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Find the equation for the ellipse that given that satisfies the given conditions: Length of minor axis 16, foci (0,±6).
Find the equation of the normal to the ellipse a2x2+b2y2=1
at the positive end of the latus rectum.
Find the coordinates of the focus, axis of the parabola ,the equation of directrix and the length of the latus reactum for x 2 =6y
If the line lx+my+n=0
cuts the ellipse (a2x2)+(b2y2)=1
at points whose eccentric angles differ by 2π,
then find the value of n2a2l2+b2m2
Find the point (α,β)
on the ellipse 4x2+3y2=12,
in the first quadrant, so that the area enclosed by the lines y=x,y=β,x=α
, and the x-axis is maximum.
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.
constant, then the locus of the point of intersection of tangents at P(acosα,bsinα)
to the ellipse a2x2+b2y2=1
(a) a circle
(b) a straight line
(c) an ellipse
(d) a parabola
Tangents are drawn to the ellipse a2x2+b2y2=1,(a>b), and the circle x2+y2=a2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan−1(2aba−b) (B) tan−1(2aba+b) (C) tan−1(a−b2ab) (D) tan−1(a+b2ab)