AP EAMCET · Maths · Pair of Lines
Two of the lines represented by the equation \(a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4=0\) will be perpendicular, then
- A \((b+d)(a d+b e)+(e-a)^2(a+c+e)=0\)
- B \((b+d)(a d+b e)+(e+a)^2(a+c+e)=0\)
- C \((b-d)(a d-b e)+(e-a)^2(a+c+e)=0\)
- D \((b-d)(a d-b e)+(e+a)^2(a+c+e)=0\)
Answer & Solution
Correct Answer
(A) \((b+d)(a d+b e)+(e-a)^2(a+c+e)=0\)
Step-by-step Solution
Detailed explanation
Let \(a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4\) \(=\left(a x^2+p x y-a y^2\right)\left(x^2+q x y+y^2\right)\) Comparing the coefficients of similar terms, b = aq − p, c = − pq, d = aq + p and e = − a b + d = 2aq and e − a = − 2a ad + be = 2ap and a + c + e = − pq…
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