Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202618 April 2026Morning ShiftMathematicsCircleActual

The area of the region (in sq. unit) bounded by x-axis, the tangent and normal to the circle x^2 + y^2 = 4 , drawn at a point (1, 3 ) is

Options

  1. A5
  2. B3
  3. C2
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

Equation of the circle is x^2 + y^2 = 4 . Equation of the tangent at the point (1, 3 ) is given by xx₁ + yy₁ = r^2 , which is x + 3 y = 4 . Equation of the normal at (1, 3 ) passes through the origin (0,0) , so its equation is y = 3 x . The region bounded by the tangent, normal, and the x-axis ( y=0 ) forms a triangle. We find its vertices by solving the equations of the lines pairwise. Intersection of the normal and the x-axis is (0, 0) . Intersection of the tangent and the x-axis is obtained by putting y=0 in x +

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 MHT CET PYQs