Tangent to an ellipse

JEE Main Mathematics · Ellipse · 6 questions, latest first

• If the line α x+4 y=√7, where α ∈ R, touches the ellipse 3 x^2+4 y^2=1 at the point P in the first quadrant, then one of the…202621 January, Shift 2 · Q13
• Let for two distinct values of p the lines y=x+p touch the ellipse E: x^2/4^2+y^2/3^2=1 at the points A and B. Let the line y=x…20254 April, Shift 2 · Q10
• Let a circle of radius 4 be concentric to the ellipse 15 x^2+19 y^2=285. Then the common tangents are inclined to the minor axis…202310 April, Shift 2 · Q13
• The line x=8 is the directrix of the ellipse E: x^2/(a^2)+y^2/(b^2)=1 with the corresponding focus (2,0). If the tangent to E at…20231 February, Shift 2 · Q89
• If the tangent at a point P on the parabola y^2=3 x is parallel to the line x+2 y=1 and the tangents at the points Q and R on the…202329 January, Shift 2 · Q72
• Let a tangent to the curve 9 x^2+16 y^2=144 intersect the coordinate axes at the points A and B. Then, the minimum length of the…202324 January, Shift 1 · Q81