Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201726 Apr 2017Morning ShiftMathematicsStraight LinesActual

A circle having centre at the origin passes through the three vertices of an equilateral triangle the length of its median being 9 units. Then the equation of that circle is

Options

  1. Ax^2+y^2=9
  2. Bx^2+y^2=18
  3. Cx^2+y^2=36
  4. Dx^2+y^2=81

Correct answer

C. x^2+y^2=36

Step-by-step solution

We have, length of median of A B C=9 A O= 2 3 A D A O= 2 3 9=6 O is the circumcentre of A B C . We know that in equilateral triangle circumcentre, incentre, centroid coincide. Origin O(0,0) is the centre and A O is radius of circle. Hence, equation of circle aligned & (x- )^2+(y- )^2=(6)^2 & x^2+y^2=36 aligned

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