Find common tangent of the two curve y2=4x and x2+y2−6x=0 (a) y=3x+3 (b) y=(3x−3) (c) y=3x−3 (d) y=(3x+3)
If the chord joining points P(α)andQ(β) on the ellipse (a2x2)+(b2y2)=1 subtends a right angle at the vertex A(a,0), then prove that tan(2a)tan(2β)=−a2b2˙
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?
A line passing through the origin O(0,0) intersects two concentric circles of radii aandb at PandQ, If the lines parallel to the X-and Y-axes through QandP, respectively, meet at point R, then find the locus of R˙
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
The auxiliary circle of a family of ellipses passes through the origin and makes intercepts of 8 units and 6 units on the x and y-axis, respectively. If the eccentricity of all such ellipses is 21, then find the locus of the focus.