AP EAMCET · Maths · Parabola

Equation of the directrix of the parabola whose focus is $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is

A $x - y = 0$
B $x - y - 1 = 0$
C $x - y + 2 = 0$
D $x + y - 1 = 0$

Verified Solution

Answer & Solution

Correct Answer

(C) $x - y + 2 = 0$

Step-by-step Solution

Detailed explanation

We have, x-y+1=0 ...i Focus is (0,0). Perpendicular distance from (0,0) to (i) is given by d=0-0+112+12=12 Now, equation of directrix is given by x-y+c=0 [ ∵ directrix is parallel to tangent at vertex ] Perpendicular distance from (0,0) to directrix is…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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Equation of the directrix of the parabola whose focus is (0,0) and the tangent at the vertex is x-y+1=0 is

Step-by-step Solution

Equation of the directrix of the parabola whose focus is $(0, 0)$ and the tangent at the vertex is $x - y + 1 = 0$ is