Home
Class 12
MATHS
The locus a point P(alpha,beta) moving u...

The locus a point `P(alpha,beta)` moving under the condition that the line `y=alphax+beta` is a tangent to the hyperbola `x^2/a^2-y^2/b^2=1` is (A) a parabola (B) an ellipse (C) a hyperbola (D) a circle

Text Solution

Verified by Experts

The correct Answer is:
`(x^(2))/(b^(2)//a^(2))-(y^(2))/(b^(2))=1`
The line `y=alphax+beta` touches the hyperbola
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
If `beta^(2)=a^(2)alpha^(2)-b^(2).`
Hence, the locus of `(alpha, beta)` is
`y^(2)=a^(2)x^(2)-b^(2)`
`"or "a^(2)x^(2)-y^(2)=b^(2)`
`"or "(x^(2))/(b^(2)//a^(2))-(y^(2))/(b^(2))=1`
which is a hyperbola
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.4|5 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.5|5 Videos

  • HYPERBOLA

    CENGAGE|Exercise Exercise 7.2|12 Videos

  • HIGHT AND DISTANCE

    CENGAGE|Exercise JEE Previous Year|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Question Bank|21 Videos

Similar Questions

Explore conceptually related problems

The values of 'm' for which a line with slope m is common tangent to the hyperbola x^2/a^2-y^2/b^2=1 and parabola y^2 = 4ax can lie in interval:

Which of the following can be slope of tangent to the hyperbola 4x^2-y^2=4? (a)1 (b) -3 (c) 2 (d) -3/2

The locus of a point whose chord of contact with respect to the circle x^2+y^2=4 is a tangent to the hyperbola x y=1 is a/an ellipse (b) circle hyperbola (d) parabola

Find the locus of the-mid points of the chords of the circle x^2 + y^2=16 , which are tangent to the hyperbola 9x^2-16y^2= 144

The locus of the point of intersection of the tangent at the endpoints of the focal chord of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 ( b < a) (a) is a an circle (b) ellipse (c) hyperbola (d) pair of straight lines

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

The locus of the point of intersection of perpendicular tangents to the hyperbola x^(2)/16 - y^(2)/9 = 1 is _____

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0), y_(0)).

The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(25)-(y^(2))/(9) is:

Find the condition on aa n db for which two distinct chords of the hyperbola (x^2)/(2a^2)-(y^2)/(2b^2)=1 passing through (a , b) are bisected by the line x+y=b .