AP EAMCET · Maths · Straight Lines
If \(A=(a, 0)\) and \(B=(-a, 0)\), then the locus of a point \(\mathrm{P}\) such that \(\mathrm{PA}^2-\mathrm{PB}^2=a^2\) is.
- A a circle
- B an ellipse
- C a hyperbola
- D a straight line
Answer & Solution
Correct Answer
(D) a straight line
Step-by-step Solution
Detailed explanation
Let \\(P=(x, y)\\). \\(PA^2 - PB^2 = a^2\\) \\((x-a)^2 + y^2 - ((x+a)^2 + y^2) = a^2\\) \\((x^2 - 2ax + a^2) - (x^2 + 2ax + a^2) = a^2\\) \\(-4ax = a^2\\) \\(x = -\frac{a}{4}\\) A straight line.
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