AP EAMCET · Maths · Parabola
The equation of the parabola with focus \((0,0)\) and directrix \(x+y=4\) is
- A \(x^2+y^2-2 x y+8 x+8 y-16=0\)
- B \(x^2+y^2-2 x y+8 x+8 y=0\)
- C \(x^2+y^2+8 x+8 y-16=0\)
- D \(x^2-y^2+8 x+8 y-16=0\)
Answer & Solution
Correct Answer
(A) \(x^2+y^2-2 x y+8 x+8 y-16=0\)
Step-by-step Solution
Detailed explanation
Given focus of parabola is \(S(0,0)\). Equation of directrix is \(x+y=4\) Let \(P(x, y)\) be any point on the parabola. Now, \(S P^2=P M^2\) \(\Rightarrow \quad(x-0)^2+(y-0)^2=\left[\frac{x+y-4}{\sqrt{1+1}}\right]^2\) \(\Rightarrow \quad x^2+y^2=\frac{(x+y-4)^2}{2}\)…
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