Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET2011MathematicsStraight Lines

The locus of a point such that the sum of its distances from the points (0,2) and (0,-2) is 6 , is

Options

  1. A9 x^2-5 y^2=45
  2. B5 x^2+9 y^2=45
  3. C9 x^2+5 y^2=45
  4. D5 x^2-9 y^2=45

Correct answer

C. 9 x^2+5 y^2=45

Step-by-step solution

Let P (x₁, y₁ ) be any point, then aligned (x₁-0 )^2+ & (y₁-2 )^2 & + (x₁-0 )^2+ (y₁+2 )^2 =6 aligned aligned & x₁^2+ (y₁-2 )^2 =6- x₁^2+ (y₁+2 )^2 & x₁^2+ (y₁-2 )^2=36+ (x₁^2+ (y₁+2 )^2 ) & -12 x₁^2+ (y₁+2 )^2 & -8 y₁=36-12 x₁^2+ (y₁+2 )^2 & 3 x₁^2+ (y₁+2 )^2 =2 y₁+9 & 9 (x₁^2+ (y₁+2 )^2 )=4 y₁^2+81+36 y₁ & 9 x₁^2+5 y₁^2=45 aligned Hence, locus of a point is 9 x^2+5 y^2=45

Practice Straight Lines on Quantrex Academy →

More from Straight Lines

The locus of the third vertex of a right-angled triangle, the ends of whose hypotenuse are (1,2) and (4,5) , is 2025The coordinate axes are rotated about the origin in the counter clockwise direction through an angle 60^ . If a and b are the intercepts made on the new axes by a straight line who 2025The image of a point (2,-1) with respect to the line x-y+1=0 is 2025If a straight line is at a distance of 10 units from the origin and the perpendicular drawn from the origin to it makes an angle 4 with the negative X -axis in the negative directi 2025A straight line passing through the origin O meets the parallel lines 4 x+2 y=9 and 2 x + y +6=0 at the points P and Q respectively. Then the point O divides the line segment PQ in 2025A (4,3), B (2,5) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoi 2025By shifting the origin to the point (2,3) through translation of axes, if the equation of the curve x^2+3 x y-2 y^2+4 x-y-20=0 is transformed to the form Ax ^2+ Bxy + Cy ^2+ Dx + E 2025The points (2,3) and (-4,- 4 3 ) lie on the opposite sides of the line L 5 x -6 y + k =0 and k is an integer. If the points (1,2) and (4,5) lie on the same side of the line L =0 , 2025 Full Straight Lines list All AP EAMCET PYQs