TS EAMCET · Maths · Parabola

If $y^{2} = 16 x$ is the given parabola, then the point of intersection of the focal chord through the point $(2, 2)$ and the double ordinate of length $24$ is

A $(3, 1)$
B $(9, - 5)$
C $(9, 3)$
D $(8, - 4)$

Verified Solution

Answer & Solution

Correct Answer

(B) $(9, - 5)$

Step-by-step Solution

Detailed explanation

Given parabola y2=16x, So focus will be 4,0, Now equation of focal chord passing through 2,2 and focus 4,0 will be y=-22x-4⇒y+x=4 .......1 Now given length of double ordinate is 24, So 2y=24⇒y=12 putting in parabola equation we get, 122=16x⇒x=9 Now putting…

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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If y2=16x is the given parabola, then the point of intersection of the focal chord through the point 2,2 and the double ordinate of length 24 is

Step-by-step Solution

If $y^{2} = 16 x$ is the given parabola, then the point of intersection of the focal chord through the point $(2, 2)$ and the double ordinate of length $24$ is