Ellipse JEE Advanced Quiz
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Question 1 of 15
1. Question
3 pointsA focus of an ellipse is at the origin. The directrix is the line x=4 and the eccentricity is 0.5. Then the length of the semimajor axis is
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Question 2 of 15
2. Question
3 pointsEquation of the circle passing through the foci of the ellipse (x^{2}/16) + (y^{2}/9)=1 and having centre at (0,3) is :
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Question 3 of 15
3. Question
3 pointsThe value of k , if (1,2),(k,−1) are conjugate points with respect to the ellipse 2x^{2}+3y^{2}=6 is
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Question 4 of 15
4. Question
3 pointsIf the curves b^{2}x^{2 }+ a^{2}y^{2}=a^{2}b^{2} and 16x^{2}+25y^{2}=400 cut each other orthogonally, then a^{2}−b^{2}=
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Question 5 of 15
5. Question
3 pointsThe locus of a point such that the sum of its distance from the points (0,2) and (0,2) is 6,is
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Question 6 of 15
6. Question
3 pointsThe length of the latus rectum of the conic 5=2r+3rcosθ+4rsinθ is :
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Question 7 of 15
7. Question
3 pointsIf tangents are drawn from any point on the circle x^{2}+y^{2}=25 to the ellipse 9x^{2}+16y^{2}=144, then the angle between the tangents is
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Question 8 of 15
8. Question
3 pointsLet a and b be nonzero real numbers. Then, the equation (ax^{2}+by^{2}+c)(x^{2}–5xy+6y^{2}) = 0 represents
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Question 9 of 15
9. Question
3 pointsThe minimum area of a triangle formed by any tangent to the ellipse 81x^{2}+16y^{2}=1296 and the coordinate axes is:
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Question 10 of 15
10. Question
3 pointsIf the line 2x+5y=12 intersects the ellipse 4x^{2}+5y^{2}=20 in two distinct points A and B, then midpoint of AB is
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Question 11 of 15
11. Question
3 pointsThe ellipse E1: 4x^{2}+9y^{2}=36 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E_{2} passing through the point (0,4) circumscribes the rectangle R. The eccentricity of the ellipse E_{2 }is
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Question 12 of 15
12. Question
3 pointsStatement 1 : An equation of a common tangent o the parabola y^{2}=(16√3)x and the ellipse 2x^{2}+y^{2}=4 is y=2x+2√3.
Statement 2: If the line my=m^{2}x + (4√3),(m≠0) is a common tangent o the parabola y^{2}=(16√3)x and the ellipse 2x^{2}+y^{2}=4,then m satisfies m^{4}+2m^{2}=24.
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Question 13 of 15
13. Question
3 pointsIf the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity of the conic is ?
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Question 14 of 15
14. Question
3 pointsTangents are drawn from the point P (3,4) to the ellipse 4x^{2}+9y^{2}=36 touching the ellipse at the points A and B.
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Question 15 of 15
15. Question
3 pointsAn ellipse intersects the hyperbola 2x^{2}–2y^{2}=1 orthogonally. The eccentricity of the ellipse is reciprocal of that of the hyperbola. If the axes of the ellipse are along the coordinates axes, then
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