Ellipse JEE Advanced Quiz
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- Question 1 of 15
1. Question3 points
A 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 semi-major axis isCorrectIncorrect
- Question 2 of 15
2. Question3 points
Equation of the circle passing through the foci of the ellipse (x2/16) + (y2/9)=1 and having centre at (0,3) is :CorrectIncorrect
- Question 3 of 15
3. Question3 points
The value of k , if (1,2),(k,−1) are conjugate points with respect to the ellipse 2x2+3y2=6 isCorrectIncorrect
- Question 4 of 15
4. Question3 points
If the curves b2x2 + a2y2=a2b2 and 16x2+25y2=400 cut each other orthogonally, then a2−b2=CorrectIncorrect
- Question 5 of 15
5. Question3 points
The locus of a point such that the sum of its distance from the points (0,2) and (0,-2) is 6,isCorrectIncorrect
- Question 6 of 15
6. Question3 points
The length of the latus rectum of the conic 5=2r+3rcosθ+4rsinθ is :CorrectIncorrect
- Question 7 of 15
7. Question3 points
If tangents are drawn from any point on the circle x2+y2=25 to the ellipse 9x2+16y2=144, then the angle between the tangents isCorrectIncorrect
- Question 8 of 15
8. Question3 points
Let a and b be non-zero real numbers. Then, the equation (ax2+by2+c)(x2–5xy+6y2) = 0 representsCorrectIncorrect
- Question 9 of 15
9. Question3 points
The minimum area of a triangle formed by any tangent to the ellipse 81x2+16y2=1296 and the co-ordinate axes is:CorrectIncorrect
- Question 10 of 15
10. Question3 points
If the line 2x+5y=12 intersects the ellipse 4x2+5y2=20 in two distinct points A and B, then mid-point of AB isCorrectIncorrect
- Question 11 of 15
11. Question3 points
The ellipse E1: 4x2+9y2=36 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse E2 passing through the point (0,4) circumscribes the rectangle R. The eccentricity of the ellipse E2 isCorrectIncorrect
- Question 12 of 15
12. Question3 points
Statement 1 : An equation of a common tangent o the parabola y2=(16√3)x and the ellipse 2x2+y2=4 is y=2x+2√3.
Statement 2: If the line my=m2x + (4√3),(m≠0) is a common tangent o the parabola y2=(16√3)x and the ellipse 2x2+y2=4,then m satisfies m4+2m2=24.CorrectIncorrect
- Question 13 of 15
13. Question3 points
If 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 ?CorrectIncorrect
- Question 14 of 15
14. Question3 points
Tangents are drawn from the point P (3,4) to the ellipse 4x2+9y2=36 touching the ellipse at the points A and B.CorrectIncorrect
- Question 15 of 15
15. Question3 points
An ellipse intersects the hyperbola 2x2–2y2=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, thenCorrectIncorrect