Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
COMEDK2012MathematicsCircle

If the area of the circle 7 x²+7 y²-7 x+14 y+k-0 is 12 sq units, then the value of k is

Options

  1. A-43 4
  2. B-301 4
  3. C-16
  4. D4

Correct answer

B. -301 4

Step-by-step solution

We have, aligned 7 x²+7 y²-7 x+14 y+k &=0 x²+y²-x+2 y+ k 7 &=0 aligned Here, C ( 1 2 ,-1 ) and r= 1 4 +1- k 7 r= 5 4 - k 7 Given that, Area =12 sq . unit 12 = ( 5 4 - k 7 ) 12= 5 4 - k 7 12= 35-4 k 28 336=35-4 k 4 k=-301 k=- 301 4

Practice Circle on Quantrex Academy →

More from Circle

A circle touches both the coordinate axes and the straight line L 4 x +3 y -6=0 in the first quadrant. If this circle lies below the line L =0 , then the equation of that circle is 2025If the smallest circle through the points of intersection of x^2+y^2=a^2 and x +y =p, 0 < p < a is x^2+y^2-a^2+ (x +y -p)=0 then = 2025If the lines 3 x-4 y+4=0 and 6 x-8 y-7=0 are the tangents to the same circle, then the area of that circle (in sq.units) is 2025Circles are drawn through the point (2,0) to cut intercepts of length 5 units on the X -axis. If their centre lie in the first quadrant, then their equation is 2025The circles x^2+y^2-2 x-4 y-4=0 and x^2+y^2+2 x+4 y-11=0 2025If the line 4 x-3 y+7=0 touches the circle x^2+y^2-6 x+4 y-12=0 at ( , ) , then +2 = 2025The slope of the common tangent drawn to the circles x^2+y^2-4 x+12 y-216=0 and x^2+y^2+6 x-12 y+36=0 is 2025If r₁ and r₂ are radii of two circles touching all the four circles (x r)^2+(y r)^2=r^2 , then r₁+r₂ r = 2025 Full Circle list All COMEDK PYQs