Questions

$A common tangent to the conics x^{2} = 6 y and 2 x^{2} - 4 y^{2} = 9 is$

Remember concepts with our Masterclasses.

80k Users

60 mins Expert Faculty Ask Questions

x+y=1

x−y=1

x+y=92

x−y=32

Ready to Test Your Skills?

Check Your Performance Today with our Free Mock Tests used by Toppers!

detailed solution

Correct option is D

Let y=(mx+c) is tangent to x2=6ysolve the above equations ⇒x2=6(mx+c) So, x2−6mx−6c=0 Put D=b2−4ac=0⇒c=−32m2∴ we get y=mx−32m2…….(1) And given hyperbola equation is 2x2−4y2=9⇒x292−y294=1….(2) Since, equation (1) is a tangent of equation (2) then c2=a2m2−b2⇒94m4=92m2−94⇒m4=2m2−1⇒m4−2m2+1=0⇒m2−12=0⇒m=±1 for m=1 , equation of tangent is x−y=32Therefore, the correct answer is (D).

Talk to our academic expert!

Create Your Own Test
Your Topic, Your Difficulty, Your Pace

Similar Questions

Statement-1: The locus of the point of intersection of the tangents that are at right angles to the hyperbola $\frac{x^{2}}{36} - \frac{y^{2}}{16} = 1 is the circle x^{2} + y^{2} = 52$

Statement-2: Perpendicular tangents to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ interest on the director circle $x^{2} + y^{2} = a^{2} - b^{2} (a^{2} > b^{2})$ of the hyperbola.