AP EAMCET · Maths · Parabola
If the tangent drawn to the parabola \(y^2=4 x\) at \(\left(t^2, 2 t\right)\) is the normal to the ellipse \(4 x^2+5 y^2=20\) at \((\sqrt{5} \cos \theta, 2 \sin \theta)\), then
- A \(5 t^4+4 t^2=1\)
- B \(\frac{5}{t^4}+\frac{100}{t^2}=1\)
- C \(t=\sin \theta\)
- D \(\cos \theta=t+1\)
Answer & Solution
Correct Answer
(A) \(5 t^4+4 t^2=1\)
Step-by-step Solution
Detailed explanation
Given, tangent to parabola \(y^2=4 x\) at \(\left(t^2, 2 t\right)\) is \[ y \cdot 2 t=2\left(x+t^2\right) \Rightarrow y t=x+t^2 \] Normal to the ellipse \(4 x^2+5 y^2=20\) or \(\frac{x^2}{5}+\frac{y^2}{4}=1\) at \((\sqrt{5} \cos \theta, 2 \sin \theta)\) \(\Rightarrow\) Slope of…
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