Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202316 May 2023Evening ShiftMathematicsStraight LinesActual

Let the curve x^2+2 y^2=2 intersect the line x+y=1 at two points P and Q and O be the origin. If is the acute angle between the lines OP and OQ , then =

Options

  1. A1 4
  2. B4
  3. C3
  4. D1 3

Correct answer

B. 4

Step-by-step solution

Given the curve x^2+2 y^2=2 & x+y=1 aligned & x^2+2 y^2=2 x^2+2 y^2=2(1)^2 & x^2+2 y^2=2(x+y)^2 & x^2+2 y^2=2 x^2+2 y^2+4 x y x^2+4 x y=0 aligned Now, = | 2 h^2-a b a+b |= | 2 2^2-0 1+0 |=4 =4

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