Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from (1,2) on surface of parabola. If focus of parabola is (2,2+√3), then length of latus rectum will be

Question

Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from (1,2) on surface of parabola. If focus of parabola is (2,2+√3), then length of latus rectum will be (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

∵ Light rays after reflection passes through focus and reflected ray is parallel to directrix. ∴ point (1,2) will be one extremity of LR. ∴ Length of L R=2 √(2-1)2+(2+√3-2)2=4

Q. Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from $(1, 2)$ on surface of parabola. If focus of parabola is $(2, 2 + 3)$ , then length of latus rectum will be

1

2

3

4

$∵$ Light rays after reflection passes through focus and reflected ray is parallel to directrix.
$∴$ point $(1, 2)$ will be one extremity of LR.
$∴$ Length of $L R = 2 (2 - 1)^{2} + (2 + 3 - 2)^{2} = 4$

Q. Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from (1,2) on surface of parabola. If focus of parabola is (2,2+3​), then length of latus rectum will be

1

2

3

4

∵ Light rays after reflection passes through focus and reflected ray is parallel to directrix. ∴ point (1,2) will be one extremity of LR. ∴ Length of LR=2(2−1)2+(2+3​−2)2​=4

Q. Aray of light travelling along a line parallel to axis of parabola and moves along parallel to directrix after reflection from $(1, 2)$ on surface of parabola. If focus of parabola is $(2, 2 + 3)$ , then length of latus rectum will be

$∵$ Light rays after reflection passes through focus and reflected ray is parallel to directrix.
$∴$ point $(1, 2)$ will be one extremity of LR.
$∴$ Length of $L R = 2 (2 - 1)^{2} + (2 + 3 - 2)^{2} = 4$