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jee_main_2025_04_april_evening - Conic Sections Topics

Master these core formulas and structures to solve almost any past paper question.

Sample Questions in this Chapter

QUESTION #57 Parabola
The axis of a parabola is the line y = x and its vertex and focus are in the first quadrant at distances sqrt2 and 2sqrt2 units from the origin, respectively. If the point (1, k) lies on the parabola, then a possible value of k is:
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QUESTION #60 Hyperbola
Let the sum of the focal distances of the point mathrmP(4,3) on the hyperbola mathrmH:fracmathrmx^2mathrma^2 -fracmathrmy^2mathrmb^2 = 1 be 8sqrtfrac53. If for mathrmH, the length of the latus rectum is l and the product of the focal distances of the point mathrmP is mathfrakm, then 9l^2 + 6mathrmm is equal to:
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QUESTION #64 Ellipse
Let for two distinct values of p the lines y = x + p touch the ellipse E: fracx^24^2 + fracy^23^2 = 1 at the points A and B. Let the line y = x intersect E at the points C and D. Then the area of the quadrilateral ABCD is equal to
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QUESTION #67 Ellipse Properties
The centre of a circle C is at the centre of the ellipse E: fracx^2a^2 + fracy^2b^2 = 1, a > b. Let C pass through the foci F_1 and F_2 of E such that the circle C and the ellipse E intersect at four points. Let P be one of these four points. If the area of the triangle PF_1F_2 is 30 and the length of the major axis of E is 17, then the distance between the foci of E$ is :
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