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Suppose that the foci of the ellipse (x^...

Suppose that the foci of the ellipse `(x^2)/9+(y^2)/5=1` are `(f_1,0)a n d(f_2,0)` where `f_1>0a n df_2<0.` Let `P_1a n dP_2` be two parabolas with a common vertex at (0, 0) and with foci at `(f_1 .0)a n d` (2f_2 , 0), respectively. Let`T_1` be a tangent to `P_1` which passes through `(2f_2,0)` and `T_2` be a tangents to `P_2` which passes through `(f_1,0)` . If `m_1` is the slope of `T_1` and `m_2` is the slope of `T_2,` then the value of `(1/(m1 2)+m2 2)` is

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Suppose that the foci of the ellipse (x^(2))/(9)+(y^(2))/(5)=1 are (f_(1),0) and (f_(2),0) where f_(1)gt0 and f_(2)lt0 Let P_(1) and P_(2) be two parabola with a c ommon vertex at (0, 0) and with foci at (f_(1),0) and (2f_(z),0) and T_(2) be a tangent to P_(2) which passes through (f_(1),0) . If m_(1) is the slope of T_(1) and m_(2) is the slope of T_(2) , then the value of ((1)/(m_(1)^(2))+m_(2)^(2)) , is

F_(1) and F_(2) are the two foci of the ellipse (x^(2))/(9) + (y^(2))/(4) = 1. Let P be a point on the ellipse such that |PF_(1) | = 2|PF_(2)| , where F_(1) and F_(2) are the two foci of the ellipse . The area of triangle PF_(1)F_(2) is :

Let P be a variable on the ellipse (x^(2))/(25)+ (y^(2))/(16) =1 with foci at F_(1) and F_(2)

Let F_1(x_1,0) and F_2(x_2,0), for x_1 0, be the foci of the ellipse x^2/9+y^2/8=1 Suppose a parabola having vertex at the origin and focus at F_2 intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant. If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF_1 NF_2 is

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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