Auxiliary Circle of Ellipse
Trending Questions
Q.
The locus of the point of intersection of the lines ax sec θ+by tanθ=a and ax tanθ+by secθ=b, where θ is the parameter, is
A straight line
A circle
An ellipse
A hyperbola
Q. The tangent at any point on the ellipse x2a2+y2b2=1 meets the auxiliary circle at two points which subtend a right angle at the centre. When the eccentricity of the ellipse is minimum then
- the y− intercept made by the tangent is y=±b√2 when a>b
- the x− intercept made by the tangent is x=±a√2 when a<b
- minimum value of eccentricity is 1√2
- When a>b, then the area enclosed between the tangents and the ellipse is (4−π)ab
Q. The auxiliary circle of family of ellipses, passes through origin and makes intercept of 8 and 6 units on the x− axis and the y− axis respectively. If eccentricity of all such family of ellipse is 12, then the locus of focus of ellipse will be
- 4x2+4y2+32x−24y+75=0
- 4x2+4y2−32x−24y+75=0
- 4x2+4y2−32x+24y+75=0
- 4x2+4y2−32x−24y−75=0
Q.
Equation of the locus of the pole with respect to the ellipse x2a2+y2b2=1 of any tangent line to the auxiliary circle is the curve
x2a4+y2b4=λ2 where
λ2=a2
λ2=1a2
λ2=b2
λ2=1b2
Q. If the ellipse x24+y2=1 meets the ellipse x2+y2a2=1 in four distinct points and a=b2−5b+7, then b does not lie in
- [4, 5]
- (−∞, 2)∪(3, ∞)
- (−∞, 0)
- [2, 3]