Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Evening ShiftMathematicsStraight LinesActual

Suppose P and Q are the mid points of the sides A B and B C of a triangle where A 1 , 3 , B 3 , 7 and C 7 , 15 are vertices. Then the locus of R satisfying A C 2 + Q R 2 = P R 2 is

Options

  1. A6 x + 12 y = 297
  2. B6 x + 12 y + 297 = 0
  3. C12 x + 6 y = 297
  4. D12 x + 6 y + 297 = 0

Correct answer

A. 6 x + 12 y = 297

Step-by-step solution

Given, P and Q are the mid points of the sides A B and B C of a triangle where A 1 , 3 ,   B 3 , 7 and C 7 , 15 are vertices, So, coordinates of P are 3 + 1 2 , 7 + 3 2 = 2 , 5 and of Q are 3 + 7 2 , 7 + 15 2 = 5 , 11 . Let the coordinates of R be x , y , Then A C 2 + Q R 2 = P R 2 ⇒ P R 2 - Q R 2 = A C 2 ⇒ x - 2 2 + y - 5 2 - x - 5 2 + y - 11 2 = 7 - 1 2 + 15 - 3 2 ⇒ 6 x + 12 y + 4 - 121 = 36 + 144 ⇒ 6 x + 12 y = 297 which is the locus of R

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