JEE Main2013MathematicsEllipseActual

Equation of the line passing through the points of intersection of the parabola x^2=8 y and the ellipse x^2 3 +y^2=1 is :

Options

Ay-3=0
By+3=0
C3 y+1=0
D3 y-1=0

Correct answer

D. 3 y-1=0

Step-by-step solution

x^2=8 y x^2 3 +y^2=1 From (i) and (ii), 8 y 3 +y^2=1 y=-3, 1 3 When y=-3 , then x^2=-24 , which is not possible. When y= 1 3 , then x= 2 6 3 Point of intersection are ( 2 6 3 , 1 3 ) and (- 2 6 3 , 1 3 ) Required equation of the line, y- 1 3 =0 3 y-1=0

Practice Ellipse on Quantrex Academy →

More from Ellipse

Consider the ellipse E given by x^2 18 + y^2 12 = 1 . Let H be the hyperbola whose eccentricity is the reciprocal of the eccentricity of E and whose foci are the same as that of E 2026 Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let P be the point in the first quadrant where the given ellipses intersect. If is the acute a 2026 Let x^2 f(a^2+7a+3) + y^2 f(3a+15) = 1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing positive function on R . If the set of all possible valu 2026 The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices are x = 4 6 3 . Let H: x^2 a^2 - y^2 b^2 = 1 be a hyperbola whose eccentricity is equal to t 2026 Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity is 1 3 . Let P( , 0) , > 0 , be a focus of E and AB be a chord passing through P . Then th 2026 Let a focus of the ellipse E: x^2 a^2 + y^2 b^2 = 1 be S(4, 0) and its eccentricity be 4 5 . If the point P(3, ) lies on E and O is the origin, then the area of POS is equal to: 2026 Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 + y^2 = 36 internally. Let the curve C be the locus of the point B. If the eccentricity of C is 2026 Let an ellipse x^2 a^2 + y^2 b^2 = 1 , a < b , pass through the point (4, 3) and have eccentricity 5 3 . Then the length of its latus rectum is : 2026 Full Ellipse list All JEE Main PYQs