jee-main 2020 Q58

jee-main · India · session2_05sep_shift2 Conic sections Circle-Conic Interaction with Tangency or Intersection
If the line $y = mx + c$ is a common tangent to the hyperbola $\frac{x^2}{100} - \frac{y^2}{64} = 1$ and the circle $x^2 + y^2 = 36$, then which one of the following is true?
(1) $c^2 = 369$
(2) $5m = 4$
(3) $4c^2 = 369$
(4) $8m + 5 = 0$
If the line $y = mx + c$ is a common tangent to the hyperbola $\frac{x^2}{100} - \frac{y^2}{64} = 1$ and the circle $x^2 + y^2 = 36$, then which one of the following is true?\\
(1) $c^2 = 369$\\
(2) $5m = 4$\\
(3) $4c^2 = 369$\\
(4) $8m + 5 = 0$