AP EAMCET · Maths · Ellipse
The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse \(9 x^2+4 y^2=72\) at the point \((2,3)\) with the \(X\)-axis is
- A \(\frac{25}{2}\)
- B \(\frac{39}{4}\)
- C \(\frac{35}{4}\)
- D \(\frac{45}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{39}{4}\)
Step-by-step Solution
Detailed explanation
Equation of tangent at \((2,3)\) to \(9 x^2+4 y^2=72\): \(\frac{9x(2)}{72} + \frac{4y(3)}{72} = 1 \implies \frac{x}{4} + \frac{y}{6} = 1 \implies 3x+2y=12\). X-intercept of tangent: \(3x+2(0)=12 \implies x=4\). Point \(T(4,0)\). Slope of tangent \(m_t = -\frac{3}{2}\). Slope of…
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