Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Ellipse

JEE Main · Mathematics · Ellipse

The equation of an ellipse whose focus is (- 1, 1) and whose...

The equation of an ellipse whose focus is (−1,1)andwhosedirectrixis\left(- 1, 1\right) and whose directrix isx - y + 3 = 0andeccentricityisand eccentricity is\dfrac{1}{2}is−is -

Options

  1. A7x2+2xy+7y2+10x−10y+7=07x^{2} + 2xy + 7y^{2} + 10x - 10y + 7 = 0
  2. B7x2−2xy+7y2−10x+10y+7=07x^{2} - 2xy + 7y^{2} - 10x + 10y + 7 = 0
  3. C7x2−2xy+7y2−10x−10y−7=07x^{2} - 2xy + 7y^{2} - 10x - 10y - 7 = 0
  4. D7x2−2xy+7y2+10x+10y−7=07x^{2} - 2xy + 7y^{2} + 10x + 10y - 7 = 0

Correct answer

A. 7x2+2xy+7y2+10x−10y+7=07x^{2} + 2xy + 7y^{2} + 10x - 10y + 7 = 0

Step-by-step solution

Apply SPPM=e\dfrac{SP}{PM} = e . (by definition) SPPM=12\dfrac{SP}{PM} = \dfrac{1}{2}

⇒4(SP)2=PM2⇒ 4\left(SP\right)2 = PM^{2}

⇒4{(h+1)2+(k−1)2}={∣h−k+32∣}2⇒ 4\left\{\left(h + 1\right)2 + \left(k - 1\right)2\right\} = \left\{\left|h - k + \dfrac{3}{2}\right|\right\}2

⇒7x2+2xy+7y2+10x−10y+7=0⇒ 7x^{2} + 2xy + 7y^{2} + 10x - 10y + 7 = 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… JEE Advanced 2026Passage: Consider the ellipses given by x^2 + 4y^2 = 1 and 4x^2 + y^2 = 1 . Question: Let… JEE Advanced 2026Let (x^2)/(f(a^2+7a+3)) + (y^2)/(f(3a+15)) = 1 represent an ellipse with major axis along… JEE Main 2026The eccentricity of an ellipse E with centre at the origin O is 3 2 and its directrices… JEE Main 2026Let x = 9 be a directrix of an ellipse E , whose centre is at the origin and eccentricity… JEE Main 2026Let a focus of the ellipse E: (x^2)/(a^2) + (y^2)/(b^2) = 1 be S(4, 0) and its… JEE Main 2026Let A be the point (3, 0) and circles with variable diameter AB touch the circle x^2 +… JEE Main 2026Let an ellipse (x^2)/(a^2) + (y^2)/(b^2) = 1 , a < b , pass through the point (4, 3) and… JEE Main 2026An ellipse has its center at (1,-2) , one focus at (3,-2) and one vertex at (5,-2) . Then… JEE Main 2026Let the ellipse E: x^ 2 144 + y^ 2 169 =1 and the hyperbola H: x^ 2 16 - y^ 2 λ^ 2 =-1… JEE Main 2026Let the length of the latus rectum of an ellipse x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) , be 30.… JEE Main 2026Let (h, k) lie on the circle C: x^ 2 +y^ 2 =4 and the point (2 h+1,3 k+2) lie on an… JEE Main 2026Let each of the two ellipses E_ 1 : x^ 2 a^ 2 + y^ 2 b^ 2 =1,(a>b) and E_ 2 : x^ 2 ~A^ 2… JEE Main 2026Let the line y-x=1 intersect the ellipse x^ 2 2 + y^ 2 1 =1 at the points A and B. Then… JEE Main 2026Let S and S^ be the foci of the ellipse x^ 2 25 + y^ 2 9 =1 and P(α, β) be a point on the… JEE Main 2026If the line α x+4 y= 7 , where α ∈ R , touches the ellipse 3 x^ 2 +4 y^ 2 =1 at the point… JEE Main 2026 Full Ellipse list Ellipse JEE Maths PYQsJEE Mathematics PYQs All Highly selective Backlog Qs for JEE Main PYQs