Parabola questions
264 published questions with worked solutions.
- The area (in sq. units) of an equilateral triangle inscribed in the parabola y^2=8x, with one of its vertices on the vertex of...
- Let P be a point on the parabola, y^2=12x and N be the foot of the perpendicular drawn from P on the axis of the parabola. A line...
- If the common tangent to the parabolas y^2=4x and x^2=4y also touches the circle, x^2+y^2=c^2, then c is equal to :
- Let L_1 be a tangent to the parabola y^2=4(x+1) and L_2 be a tangent to the parabola y^2=8(x+2) such that L_1 and L_2 intersect...
- The centre of the circle passing through the point (0, 1) and touching the parabola y=x^2 at the point (2, 4) is :
- Let A, B and C be the vertices of a variable right angled triangle inscribed in the parabola y²=16x. Let the vertex B containing...
- Let the point P be the vertex of the parabola y=x²−6x+12. If a line passing through the point P intersects the circle...
- Let the directrix of the parabola P : y²=8x, cut the x-axis at the point A. Let B(α,β), α>1, be a point on P such that the slope...
- Let chord PQ of length 3√13 of the parabola y²=12x be such that the ordinates of points P and Q are in the ratio 1 : 2. If the...
- Let O be the vertex of the parabola y² = 4x and its chords OP and OQ are perpendicular to each other. If the locus of the...
- Consider the circle C : x² + y² = 4 and the parabola P : y² = 8x. If the set of all values of α, for which three chords of the...
- Let A, B and C be three points on the parabola y² = 6x and let the line segment AB meet the line L through C parallel to the...
- Let P(α, β) be a point on the parabola y² = 4x. If P also lies on the chord of the parabola x² = 8y whose mid-point is (1, 5/4)....
- Let P be a parabola with vertex (2, 3) and directrix 2x + y = 6. Let an ellipse E : x²/a² + y²/b² = 1, a > b, of eccentricity...
- Consider the parabola with vertex ( 1 2 , 3 4 ) and the directrix y = 1 2 . Let P be the point where the parabola meets the line...
- If the three normals drawn to the parabola, y^2=2x pass through the point (a, 0) a 0, then 'a' must be greater than :
- Let L be a tangent line to the parabola y^2=4x-20 at (6, 2). If L is also a tangent to the ellipse x^2 2 + y^2 b =1, then the...
- Let the tangent to the parabola S:y^2=2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the...
- Let y = mx + c, m > 0 be the focal chord of y^2 = –64x, which is tangent to (x+10)^2+y^2=4. Then, the value of 4 2(m+c) is equal...
- The locus of the mid-point of the line segment joining the focus of the parabola y^2=4ax to a moving point of the parabola, is...
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