Standard equation of an ellipse

JEE Main Mathematics · Ellipse · 26 questions, latest first

• Let x^2/(f(a^2+7 a+3))+y^2/(f(3 a+15))=1 represent an ellipse with major axis along y -axis, where f is a strictly decreasing…20268 April, Shift 2 · Q20
• 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, α) lies on E and O is…20265 April, Shift 1 · Q9
• Consider the parabola P: y^2=4 k x and the ellipse E: x^2/a^2+y^2/b^2=1. Let the line segment joining the points of intersection…20264 April, Shift 1 · Q22
• 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…20262 April, Shift 1 · Q10
• An ellipse has its center at (1, -2), one focus at (3, -2) and one vertex at (5, -2). Then the length of its latus rectum is:202628 January, Shift 2 · Q9
• Let the length of the latus rectum of an ellipse x^2/a^2+y^2/b^2=1,(a>b), be 30. If its eccentricity is the maximum value of the…202624 January, Shift 2 · Q10
• Let (h, k) lie on the circle C: x^2+y^2=4 and the point (2 h+1,3 k+2) lie on an ellipse with eccentricity e. Then the value of…202624 January, Shift 2 · Q23
• Let 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)+y^2/(B^2)=1,( A<B) have eccentricity 4/5. Let the…202624 January, Shift 1 · Q10
• Let the length of a latus rectum of an ellipse x^2/(a^2)+y^2/(b^2)=1 be 10. If its eccentricity is the minimum value of the…20257 April, Shift 2 · Q12
• Let e_1 and e_2 be the eccentricities of the ellipse x^2/(b^2)+y^2/25=1 and the hyperbola x^2/16-y^2/(b^2)=1, respectively. If…20257 April, Shift 2 · Q13
• The length of the latus-rectum of the ellipse, whose foci are (2,5) and (2,-3) and eccentricity is 4/5, is20254 April, Shift 1 · Q11
• If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of…20252 April, Shift 2 · Q12
• Let the ellipse E_1: x^2/(a^2)+y^2/(b^2)=1, a>b and E_2: x^2/(A^2)+y^2/(B^2)=1, A<B have same eccentricity 1/(√3). Let the…202529 January, Shift 1 · Q13
• Let E_1: x^2/9+y^2/4=1 be an ellipse. Ellipses E_i 's are constructed such that their centres and eccentricities are same as that…202528 January, Shift 1 · Q23
• Let E: x^2/(a^2)+y^2/(b^2)=1, a>b and H: x^2/(A^2)-y^2/(B^2)=1. Let the distance between the foci of E and the foci of H be 2 √3.…202522 January, Shift 2 · Q11
• Let f(x)=x^2+9, g(x)=x/(x-9) and a=f ° g(10), b=g ° f(3). If e and l denote the eccentricity and the length of the latus rectum…20249 April, Shift 1 · Q12
• Let the line 2 x+3 y-k=0, k>0, intersect the x -axis and y -axis at the points A and B, respectively. If the equation of the…20245 April, Shift 1 · Q15
• Let P be a parabola with vertex (2,3) and directrix 2 x+y=6. Let an ellipse E: x^2/a^2+y^2/b^2=1, a>b, of eccentricity 1/(√2)…202431 January, Shift 2 · Q14
• Let A(α, 0) and B(0, β) be the points on the line 5 x+7 y=50. Let the point P divide the line segment A B internally in the ratio…202430 January, Shift 2 · Q14
• If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the…202430 January, Shift 1 · Q15
• If the points of intersection of two distinct conics x^2+y^2=4 b and x^2/16+y^2/b^2=1 lie on the curve y^2=3 x^2, then 3 √3 times…202429 January, Shift 1 · Q28
• Let e_1 be the eccentricity of the hyperbola x^2/16-y^2/9=1 and e_2 be the eccentricity of the ellipse x^2/(a^2)+y^2/(b^2)=1,…202427 January, Shift 2 · Q14
• Let an ellipse with centre (1,0) and latus rectum of length 1/2 have its major axis along x -axis. If its minor axis subtends an…202315 April, Shift 1 · Q28
• Consider ellipses E_k: k x^2+k^2 y^2=1, k=1,2, …, 20. Let C_k be the circle which touches the four chords joining the end points…202311 April, Shift 1 · Q3
• Let the ellipse E: x^2+9 y^2=9 intersect the positive x - and y -axes at the points A and B respectively. Let the major axis of E…202310 April, Shift 1 · Q11
• In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the…20236 April, Shift 2 · Q2