Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2001MathematicsHyperbola

The equation 16 x^2+y^2+8 x y-74 x-78 y+212=0 represents

Options

  1. Aa circle
  2. Ba parabola
  3. Ca circle
  4. Dan ellipse

Correct answer

B. a parabola

Step-by-step solution

The given equation is 16 x^2+y^2+8 x y-74 x-78 y+212=0 On comparing with gathered a x^2+b y^2+2 h x y+2 g x+2 f y+c=0 a=16, b=1, h=4, g=-37, f=-39, c=212 Now, a b-h^2=(16)(1)-(4)^2=16-16=0 gathered Thus, the given equation represents a parabola.

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 2026In the figure Statement-I: When > 0 , the section is hyperbola Statement-II: When > 90^ , the section is ellipse Which of the following is correct? 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 2025 Full Hyperbola list All AP EAMCET PYQs