Assertion (A) : The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are respectively (1,-2) and 3 x+4 y-15=0. Then its eccentricity is \frac{1}{2}. Reason ( {\R}) : Length of the perpendicular drawn from focus of an ellipse to its corresponding directrix is \frac{a (1-e^2) }{e}. [AP EAPCET 27 May 2025 S1]

Correct Answer is : (A) and (R) are true, and (R) is the correct explanation to (A)

(A) and (R) are true, and (R) is the correct explanation to (A)

(A) and (R) are true, and (R) is not the correct explanation to (A)

AP EAPCET 27 May 2025 Shift 1 Paper

Section: Mathematics

Question : 53 of 160

Marks: +1, -0

Assertion (A) : The length of the latus rectum of an ellipse is 4. The focus and its corresponding directrix are respectively (1,−2) and 3x+4y−15=0. Then its eccentricity is ‌

.
Reason (R)‌‌ : Length of the perpendicular drawn from focus of an ellipse to its corresponding directrix is ‌

a(1−e2)

[AP EAPCET 27 May 2025 S1]

(A) and (R) are true, and (R) is the correct explanation to (A)
(A) and (R) are true, and (R) is not the correct explanation to (A)
(A) is true, (R) is false
(A) is false, (R) is true

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