Home
Class 12
MATHS
If alpha-beta is constant prove that th...

If `alpha-beta` is constant prove that the chord joining the points `alpha` and `beta` on the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))` =1 touches a fixed ellipse

Text Solution

Verified by Experts

The correct Answer is:
`k^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The line x cos alpha + y sin alpha =p is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. if

The line x cos alpha +y sin alpha =p is tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1. if

If alpha+beta=3pi , then the chord joining the points alpha and beta for the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through which of the following points? Focus (b) Center One of the endpoints of the transverse exis. One of the endpoints of the conjugate exis.

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse x^2/a^2+y^2/b^2=1 touch another fixed ellipse.

Prove that the chords of contact of pairs of perpendicular tangents to the ellipse x^2/a^2+y^2/b^2=1 touch another fixed ellipse.

Prove that the chord of contact of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 with respect to any point on the directrix is a focal chord.

If the chord joining points P(alpha) and Q(beta) on the ellipse ((x^2)/(a^2))+((y^2)/(b^2))=1 subtends a right angle at the vertex A(a ,0), then prove that tan(a/2)tan(beta/2)=-(b^2)/(a^2)dot

If alpha-beta= constant, then the locus of the point of intersection of tangents at P(acosalpha,bsinalpha) and Q(acosbeta,bsinbeta) to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 is: (a) a circle (b) a straight line (c) an ellipse (d) a parabola

Prove that the locus of the middle-points of the chords of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 which pass through a fixed point (alpha, beta) is a hyperbola whose centre is ((alpha)/(2), (beta)/(2)) .

I If a point (alpha, beta) lies on the circle x^2 +y^2=1 then the locus of the point (3alpha.+2, beta), is