Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
KCET2026MathematicsHyperbola

In the figure Statement-I: When > 0 , the section is hyperbola Statement-II: When > 90^ , the section is ellipse Which of the following is correct?

Options

  1. AStatement I is true, Statement II is false
  2. BStatement I is false, Statement II is true
  3. CBoth the Statements are true
  4. DBoth the Statements are false

Correct answer

A. Statement I is true, Statement II is false

Step-by-step solution

Let be the semi-vertical angle of the cone and be the angle between the intersecting plane and the axis of the cone. The conic sections formed by the intersection of a plane and a double cone are determined by the relationship between and : 1. If 0 2. If = , the plane is parallel to a generator of the cone, forming a parabola. 3. If 4. If = 90^ , the plane is perpendicular to the axis, forming a circle. From the above conditions, when > 0 , the section is a hyperbola. Hence, Statement-I is true. The angle is define

Practice Hyperbola on Quantrex Academy →

More from Hyperbola

The difference between the distance of any point on the hyperbola from the two foci is 16 and the eccentricity is 2 . Then the equation of the hyperbola is 2026If the line y = 2x + is a tangent to the hyperbola 36x^2 - 25y^2 = 3600 , then = 2026If the line 4x + 3y = 7 touches the hyperbola x^2 - y^2 = 7 , then the sum of the co-ordinates of the point of contact is... 2026If the eccentricity of the hyperbola x^2 a^2 - y^2 b^2 =1 passing through the point (4,6) is 2, then the equation of the tangent to this hyperbola at (4,6) is 2025A hyperbola passes through the point P ( 2 , 3 ) and has foci at ( 2,0) . Then the point that lies on the tangent drawn to this hyperbola at P is 2025If is the angle subtended by a latus rectum at the centre of the hyperbola having eccentricity 2 7 - 3 , then = 2025The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola x^2 4 - y^2 5 =1 meets the x -axis and y -axis at A and B respectively. If O is the origi 2025Let P ( a , b ) and Q ( a , b ) where + = 2 be two points on the hyperbola x^2 a^2 - y^2 b^2 =1 . If (h, k) is the point of intersection of the normals drawn at P and Q, then k = 2025 Full Hyperbola list All KCET PYQs