Minimum distance of a point (23,0) from the curve y=x is (a) 25 (b) 45 (c) 5 (d) 25
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.
How many real tangents can be drawn from the point (4, 3) to the hyperbola 16x2−9y2=1? Find the equation of these tangents and the angle between them.
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
Tangents are drawn to the ellipse from the point (a2−b2a2,a2+b2)) . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.
If ω is one of the angles between the normals to the ellipse a2x2+b2y2=1 at the point whose eccentric angles are θ and 2π+θ , then prove that sin2θ2cotω=1−e2e2