Home
Class 12
MATHS
Find the locus of a point P(alpha, beta)...

Find the locus of a point `P(alpha, beta)` moving under the condition that the line `y=ax+beta` is a tangent to the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`.

A

an ellipse

B

a circle

C

a parabola

D

a hyperbola

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 11 : Questions Asked in Previous 13 Years Exams|3 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 10 : Subjective Type Questions|4 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

Find the condition that the line x cos alpha + y sin alpha = p may be a tangent to the curve (x^2)/(a^2) + (y^2)/(b^2) = 1

The value of m, for which the line y = mx + 2 is a tangent to the hyperbola 4x^(2)-9y^(2)-36 are

Knowledge Check

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

    A
    `a^(2)cos^(2)alpha - b^(2)sin^(2)alpha =p^(2)`
    B
    `a^(2)sin^(2)alpha+b^(2)cos^(2)alpha=p^(2)`
    C
    `a^(2)cos^(2)alpha+b^(2)sin^(2)alpha=p^(2)`
    D
    `a^(2)cos^(2)alpha+b^(2)sin^(2)alpha =p`

    • Similar Questions

    Explore conceptually related problems

    Locus of the point of intersection of the tangents at the points with eccentric angles phi and (pi)/(2) - phi on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is

    Find the equations to the common tangents to the two hyperbolas (x^2)/(a^2)-(y^2)/(b^2)=1 and (y^2)/(a^2)-(x^2)/(b^2)=1

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

    Find the locus of the foot of perpendicular from the centre upon any normal to line hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 .

    Find the equations of tangent and normal to the hyperbola x^2/a^2 -y^2/b^2 =1 at the point (x_0,y_0)

    Find the equations of tangent and normal to the hyperbola x^2/a^2 -y^2/b^2 =1 at the point (x_0,y_0)

    Length of common tangents to the hyperbolas x^2/a^2-y^2/b^2=1 and y^2/a^2-x^2/b^2=1 is

    Home
    Profile