TS EAMCET · Maths · Application of Derivatives
If the curves \(a x^2+b y^2=1\) and \(c x^2+d y^2=1\) intersect orthogonally, then \(\frac{b-a}{d-c}=\)
- A \(\frac{a}{c} \cdot \frac{b}{d}\)
- B \(\frac{a+b}{c+d}\)
- C 1
- D 0
Answer & Solution
Correct Answer
(A) \(\frac{a}{c} \cdot \frac{b}{d}\)
Step-by-step Solution
Detailed explanation
Given curves \(a x^2+b y^2=1\) ...(i) and \(c x^2+d y^2=1\) ...(ii) From Eqs. (i) and (ii), \((a-c) x^2+(b-d) y^2=0\) \(\frac{x^2}{y^2}=-\left(\frac{b-d}{a-c}\right)\) ...(iii) Differentiating Eq. (i) w.r.t.' \(x^{\prime}\), we get…
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