Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length 27 on y-axis is (are)
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is one of the angles between the normals to the ellipse a2x2+b2y2=1
at the point whose eccentric angles are θ
, then prove that sin2θ2cotω=1−e2e2
Tangents are drawn from the points on the line x−y−5=0
. Then all the chords of contact pass through a fixed point. Find the coordinates.
Find the angle between the asymptotes of the hyperbola 16x2−9y2=1
Find the equation for the ellipse that satisfies the given conditions: b=3,ae=4 centre at the origin; foci on the x- axis.
is the positive quadrant of the ellipse a2x2+b2y2=1
in which OA=a,OB=b
. Then find the area between the arc AB
and the chord AB
of the ellipse.
If the normals to the ellipse a2x2+b2y2=1 at the points (X1,y1),(x2,y2)and(x3,y3) are concurrent, prove that ∣∣x1x2x3y1y2y3x1y1x2y2x3y3∣∣=0.
Find the equation for the ellipse that satisfies the given conditions: Centre at (0,0), major axis on the y-axis and passes through the points (3,2) and (1,6).
An ellipse has OB
as the semi-minor axis, FandF′
as its foci, and ∠FBF′
a right angle. Then, find the eccentricity of the ellipse.