If the tangent at any point of the ellipse a3x2+b2y2=1
makes an angle α
with the major axis and an angle β
with the focal radius of the point of contact, then show that the eccentricity of the ellipse is given by e=cosαcosβ
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In any triangle ABC, if the angle bisector of ∠Aand perpendicular bisector of BCintersect, prove that they intersect on the circumcircle of the triangle ABC
Find the equation of the parabola that satisfies the given conditions:Vertex (0, 0); focus (3,0)
XYand XprimeYprimeare two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XYat A and XprimeYprimeat B. Prove that ∠AOB = 90o
Find an equation of the circle with centre at (0,0) and radius r.
An equilateral triangle is inscribed in the parabola y2=4ax where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.
If the point (2,3),(1,1),and(x,3x)
are collinear, then find the value of x,
using slope method.
If TP and TQ are the two tangents to a circle with centre O so that ∠POQ=110∘, then ∠PTQ is equal to
Determine the ratio in which the line 3x+y−9=0
divides the segment joining the points (1,3) and (2,7)˙