AP EAMCET · Maths · Hyperbola
A tangent to the curve \(9 b^2 x^2-4 a^2 y^2=36 a^2 b^2\) makes intercepts of unit length on each of the coordinate axes, then the point \((a, b)\) lies on
- A \(x^2-y^2=1\)
- B \(x^2+y^2=1\)
- C \(4 x^2-9 y^2=1\)
- D \(4 x^2+9 y^2=1\)
Answer & Solution
Correct Answer
(C) \(4 x^2-9 y^2=1\)
Step-by-step Solution
Detailed explanation
Equation of given curve is, \[ \frac{x^2}{4 a^2}-\frac{y^2}{9 b^2}=1 \] Let at point \((2 a \sec \theta, 3 b \tan \theta)\) on the curve (i). So, equation of tangent at point is \[ \frac{x}{\frac{2 a}{\sec \theta}}+\frac{y}{-\frac{3 b}{\tan \theta}}=1 \] According to the…
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