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Statement 1: An equation of a common ...

Statement 1: An equation of a common tangent to the parabola `y^2=16sqrt(3)x` and the ellipse `2x^2+""y^2=""4""i s""y""=""2x""+""2sqrt(3)` . Statement 2: If the line `y""=""m x""+(4sqrt(3))/m ,(m!=0)` is a common tangent to the parabola `y^2=""16sqrt(3)x` and the ellipse `2x^2+""y^2=""4` , then m satisfies `m^4+""2m^2=""24` . (1) Statement 1 is false, statement 2 is true (2) Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1 (3) Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1 (4) Statement 1 is true, statement 2 is false

A

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for statement 1

B

Statement 1 is true, Statement 2 is false

C

Statement 1 is false, Statement 2 is true

D

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for statement 1.

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The correct Answer is:
D
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MOTION-ELLIPSE -Exercise - 4 | Level-I Previous Year | JEE Main
  1. In an ellipse, the distances between its foci is 6 and minor axis is 8...

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  2. A focus of an ellipse is at the origin. The directrix is the line x...

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  3. Statement 1: An equation of a common tangent to the parabola y^2=16...

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  4. An ellipse is drawn by taking a diameter of the circle (x – 1)^2 + y^2...

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  5. The equation of the circle passing through the foci of the ellipse ...

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  6. The locus of the foot of perpendicular drawn from the centre of the...

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  7. The area (in sq. units) of the quadrilateral formed by the tangents...

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  8. If the curves y^2=6x, 9x^2+by^2=16 intersect each other at right angle...

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  9. Let P(x1, y1) and Q(x2, y2), y1 < 0, y2 < 0, be the end points of the...

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  10. The line passing through the extremity A of the major axis and extremi...

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  11. The normal at a point P on the ellipse x^2+4y^2=16 meets the x-axis at...

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  12. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

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  13. Tangents are drawn from the point P(3, 4) to the ellipse x^2/9 +y^2/4 ...

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  14. Tangents are drawn from the point P(3,4) to the ellipse x^(2)/9+y^(2)/...

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  15. A vertical line passing through the point (h, 0) intersects the ellips...

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  16. Let E1 and E2, be two ellipses whose centers are at the origin.The maj...

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  17. Suppose that the foci of the ellipse (x^2)/9+(y^2)/5=1 are (f1,0)a n d...

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  18. Let F1(x1, 0) and F2(x2, 0), for x1 lt 0 and x2 gt 0, be the foci of t...

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  19. If the tangents to the ellipse at M and N meet at R and the normal to ...

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  20. Consider two straight lines, each of which is tangent to both the c...

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