TS EAMCET · Maths · Parabola
\(a x-y+c=0\) is the equation of the common tangent to the parabola \(y^2=8 \sqrt{5} x\) and the circle \(x^2+y^2=1\). If this tangent makes an acute angle with the positive \(\mathrm{X}\) - axis in the positive direction, then \(\mathrm{a}^2 \mathrm{c}^2=\)
- A 40
- B 80
- C 160
- D 20
Answer & Solution
Correct Answer
(D) 20
Step-by-step Solution
Detailed explanation
\(T: y=a x+C\) for \(y^2=8 \sqrt{5} x \Rightarrow C=\frac{2 \sqrt{5}}{a}\) for \(x^2+y^2=1 \Rightarrow C= \pm \sqrt{1+a^2}\) \(\Rightarrow C^2=1+a^2=\left(\frac{2 \sqrt{5}}{a}\right)^2 \Rightarrow 1+a^2=\frac{20}{a^2}\) Let \(a^2=t\) Let \(a^2=t\)…
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