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Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8?
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Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s...
Explanation:
Proof:
Therefore, the locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to 2sqrt(a^2 + b^2), which is option D (8).
- We have to find the locus of reflection of s1 with respect to any tangent of the ellipse.
- Let P be a point on the ellipse.
- Let T be the tangent to the ellipse at point P.
- Let Q be the reflection of s1 with respect to T.
- Then PQ will be perpendicular to T.
Proof:
- Let the equation of the ellipse be x^2/4 + y^2/1 = 1.
- Let P be a point (a, b) on the ellipse.
- The slope of the tangent to the ellipse at point P is given by -a/b.
- The equation of the tangent at point P is given by y - b = (-a/b)(x - a).
- Let Q be the reflection of s1 with respect to T.
- Then Q lies on the line passing through s1 and the point of intersection of T and the perpendicular bisector of s1P.
- The equation of this line is given by y - ((b^2 - a^2)/2b) = (-b/a)(x - 0).
- The coordinates of Q are given by (2a, 2((b^2 - a^2)/2b) - s1y).
- The distance between s1 and Q is given by sqrt((2a - s1x)^2 + (2((b^2 - a^2)/2b) - s1y - s1y)^2).
- Substituting the values of s1x and s1y, we get the distance between s1 and Q as 2sqrt(a^2 + b^2).
Therefore, the locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to 2sqrt(a^2 + b^2), which is option D (8).
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Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8?
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Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8?.
Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let s1,s2 two focii of ellipse x^2/4+ y^2=1. Locus of reflection of s1 with respect to any tangent of the ellipse is a circle with radius equal to. A) 2 B) 4 C) 6 D) 8?.
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