Standard equation of a hyperbola

JEE Main Mathematics · Hyperbola · 27 questions, latest first

• 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:…20266 April, Shift 2 · Q11
• If the eccentricity e of the hyperbola x^2/a^2-y^2/b^2=1, passing through (6,4 √3), satisfies 15(e^2+1)=34 e, then the length of…20266 April, Shift 1 · Q11
• Let the eccentricity e of a hyperbola satisfy the equation 6 e^2-11 e+3=0. If the foci of the hyperbola are (3,5) and (3,-4),…20265 April, Shift 2 · Q13
• Let H: x^2/a^2-y^2/b^2=1 be a hyperbola such that the distance between its foci is 6 and the distance between its directrices is…20264 April, Shift 2 · Q11
• Let the ellipse E: x^2/144+y^2/169=1 and the hyperbola H: x^2/16-y^2/(λ^2)=-1 have the same foci. If e and L respectively denote…202628 January, Shift 2 · Q12
• For some θ ∈(0, (π)/2), let the eccentricity and the length of the latus rectum of the hyperbola x^2-y^2 sec^2 θ=8 be e_1 and…202628 January, Shift 1 · Q25
• Let PQ be a chord of the hyperbola x^2/4-y^2/b^2=1, perpendicular to the x-axis such that OPQ is an equilateral triangle, O being…202623 January, Shift 2 · Q12
• Let the domain of the function f(x)= log_3 log_5 log_7(9 x-x^2-13) be the interval (m, n). Let the hyperbola…202623 January, Shift 1 · Q10
• Let P(10,2 √15) be a point on the hyperbola x^2/(a^2)-y^2/(b^2)=1, whose foci are S and S'. If the length of its latus rectum is…202622 January, Shift 2 · Q11
• Let the foci of a hyperbola coincide with the foci of the ellipse x^2/36+y^2/16=1. If the eccentricity of the hyperbola is 5,…202621 January, Shift 1 · Q9
• Consider the hyperbola x^2/a^2-y^2/b^2=1 having one of its focus at P(-3,0). If the latus ractum through its other focus subtends…20257 April, Shift 1 · Q23
• If the equation of the hyperbola with foci (4,2) and (8,2) is 3 x^2-y^2-α x+β y+γ=0, then α+β+γ is equal to ____.20253 April, Shift 2 · Q23
• Let one focus of the hyperbola H: x^2/(a^2)-y^2/(b^2)=1 be at (√10, 0) and the corresponding directrix be x=9/(√10). If e and l…20252 April, Shift 1 · Q10
• If A and B are the points of intersection of the circle x^2+y^2-8 x=0 and the hyperbola x^2/9-y^2/4=1 and a point P moves on the…202528 January, Shift 2 · Q12
• Let H_1: x^2/(a^2)-y^2/(b^2)=1 and H_2:-x^2/(A^2)+y^2/(B^2)=1 be two hyperbolas having length of latus rectums 15 √2 and 12 √5…202524 January, Shift 2 · Q25
• Let the circle C touch the line x-y+1=0, have the centre on the positive x -axis, and cut off a chord of length 4/(√13) along the…202523 January, Shift 1 · Q24
• Let the foci of a hyperbola be (1,14) and (1, -12). If it passes through the point (1, 6), then the length of its latus-rectum is:202522 January, Shift 1 · Q13
• Let the foci of a hyperbola H coincide with the foci of the ellipse E: ((x-1)^2)/100+((y-1)^2)/75=1 and the eccentricity of the…20249 April, Shift 2 · Q15
• Let S be the focus of the hyperbola x^2/3-y^2/5=1, on the positive x -axis. Let C be the circle with its centre at A(√6, √5) and…20248 April, Shift 2 · Q28
• Consider a hyperbola H having centre at the origin and foci on the x -axis. Let C_1 be the circle touching the hyperbola H and…20244 April, Shift 2 · Q14
• For 0<θ<π / 2, if the eccentricity of the hyperbola x^2-y^2 cosec^2 θ=5 is √7 times eccentricity of the ellipse x^2 cosec^2…20241 February, Shift 1 · Q12
• Let x^2/(a^2)+y^2/(b^2)=1, a>b be an ellipse, whose eccentricity is 1/(√2) and the length of the latusrectum is √14. Then the…20241 February, Shift 1 · Q13
• Let the foci and length of the latus rectum of an ellipse x^2/a^2+y^2/b^2=1, a>b be ( ± 5,0) and √50, respectively. Then, the…202431 January, Shift 1 · Q28
• Let P be a point on the hyperbola H: x^2/9-y^2/4=1, in the first quadrant such that the area of triangle formed by P and the two…202430 January, Shift 2 · Q15
• Let the latus ractum of the hyperbola x^2/9-y^2/b^2=1 subtend an angle of (π)/3 at the centre of the hyperbola. If b^2 is equal…202430 January, Shift 1 · Q27
• Let H_n: x^2/(1+n)-y^2/(3+n)=1, n ∈ N. Let k be the smallest even value of n such that the eccentricity of H_k is a rational…202311 April, Shift 1 · Q28
• Let H be the hyperbola, whose foci are (1 ± √2, 0) and eccentricity is √2. Then the length of its latus rectum is ____.202331 January, Shift 2 · Q74