Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202125 Aug 2021Morning ShiftMathematicsEllipseActual

The center of ellipse x^2+2 y^2-4 x+12 y+14=0 is

Options

  1. A(-2,-3)
  2. B(-2,3)
  3. C(2,-3)
  4. D(2,6)

Correct answer

C. (2,-3)

Step-by-step solution

We have, aligned & & x^2+2 y^2-4 x+12 y+14=0 & & (x-2)^2+2(y+3)^2=-14+4+18 & & (x-2)^2+2(y+3)^2=8 & & (x-2)^2 8 + (y+3)^2 8 / 2 =1 aligned Centre of ellipse is (2,-3) .

Practice Ellipse on Quantrex Academy →

More from Ellipse

The foci of a hyperbola are the same as those of the ellipse with equation 9x^2 + 16y^2 = 144 . If the length of the transverse axis of this hyperbola is 2 , then its equation is: 2026If the two ends of the major axis of an ellipse are (5, 0) and (-5, 0) and one focus lies on the line 3x - 5y - 9 = 0 , then its equation is 2026The length of the latus rectum of the curve represented by x = 3( t + t) and y = 4( t - t) is: 2026If P be any point on the ellipse 16x^2 + 25y^2 = 400 with foci S and S' and area of PSS' is 9 square units, then the abscissa of point P is........... 2026If is the eccentric angle of a point on the ellipse x^2 25 + y^2 9 = 1 such that the distance of the point from the center is 5 , then = ....... 2026The eccentricity of the ellipse represented by the equation 7x^2 + 16y^2 - 14x + 64y - 377 = 0 is... 2026A tangent having slope - 1 2 to the ellipse 3x^2 + 4y^2 = 12 intersects the X-axis and Y-axis at the points A and B respectively. if O is the origin, then the area of AOB is ... 2026If the eccentricity of the ellipse x^2 a^2 + y^2 b^2 = 1, (a > b) is 2 3 and its focal chord is 3x + 2y - 6 = 0 , then the value of a^2 + b^2 is... 2026 Full Ellipse list All AP EAMCET PYQs