Hyperbola questions
149 published questions with worked solutions.
- Let e₁ and e₂ be two distinct roots of the equation x²−ax+2=0. Let the sets a∈ℝ : e₁ and e₂ are the eccentricities of hyperbolas...
- If the eccentricity e of the hyperbola x^2 a^2 - y^2 b^2 =1, passing through (6, 4√3), satisfies 15(e²+1)=34e, then the length of...
- 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...
- Let e₁ be the eccentricity of the hyperbola x^2 16 - y^2 9 = 1 and e₂ be the eccentricity of the ellipse x^2 a^2 + y^2 b^2 = 1, a...
- Let P be a point on the hyperbola H : x²/9 − y²/4 = 1, in the first quadrant such that the area of triangle formed by P and the...
- Let the latus rectum of the hyperbola x^2 9 - y^2 b^2 = 1 subtend an angle of π/3 at the centre of the hyperbola. If b² is equal...
- Let the foci and length of the latus rectum of an ellipse x²/a² + y²/b² = 1, a > b be (± 5, 0) and √50, respectively. Then, the...
- Consider a hyperbola H : x^2-2y^2=4. Let the tangent at a point P(4, 6) meet the x-axis at Q and latus rectum at R(x_1,y_1),...
- Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x^2-y^2=3. If L is also a tangent to the parabola y^2= x, then is...
- Let A (sec , 2tan ) and B (sec , 2tan ), where + = /2, be two points on the hyperbola 2x^2-y^2=2. If ( , ) is the point of the...
- A hyperbola passes through the foci of the ellipse x^2 25 + y^2 16 =1 and its transverse and conjugate axes coincide with major...
- The locus of the centroid of the triangle formed by any point P on the hyperbola 16x^2-9y^2+32x+36y-164=0, and its foci is :
- The point P(-2 6, 3) lies on the hyperbola x^2 a^2 - y^2 b^2 =1 having eccentricity 5 2 . If the tangent and normal at P...
- The locus of the mid points of the chords of the hyperbola x^2-y^2=4, which touch the parabola y^2=8x, is :
- Let x - 2y = be a tangent to the hyperbola a^ 2 x^ 2 - y^ 2 = b^ 2 . Then ( /a)^ 2 - ( /b)^ 2 is equal to :
- Let the hyperbola H : x^ 2 /a^ 2 - y^ 2 = 1 and the ellipse E : 3x^ 2 + 4y^ 2 = 12 be such that the length of latus rectum of H...
- Let the foci of the ellipse x^ 2 /16 + y^ 2 /7 = 1 and the hyperbola x^ 2 /144 - y^ 2 / = 1/25 coincide. Then the length of the...
- Let the eccentricity of the hyperbola x^ 2 /a^ 2 - y^ 2 /b^ 2 = 1 be 5/4. If the equation of the normal at the point (8/ 5 ,...
- If the line x − 1 = 0 is a directrix of the hyperbola kx^ 2 - y^ 2 = 6, then the hyperbola passes through the point
- Let a line L_ 1 be tangent to the hyperbola x^ 2 /16 - y^ 2 /4 = 1 and let L_ 2 be the line passing through the origin and...
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