Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202017 Sep 2020Morning ShiftMathematicsCircleActual

The point on the circle (x^2+y^2=4 ) whose distance from the line (4 x+3 y-12=0 ) is (4 / 5 ) units is equal to

Options

  1. A( ( 12 25 , 36 25 ) )
  2. B((4,0) )
  3. C((2,0) )
  4. D( ( -14 25 , 48 25 ) )

Correct answer

C. ((2,0) )

Step-by-step solution

Let the point be ((h, k) ) So, ( |4 h+3 k-12| 5 = 4 5 |4 h+3 k-12|=4 ) ( (4 h+3 k=16) ) or ((4 h+3 k=8) ) ((h, k) ) lies on circle so ( aligned & h^2+k^2=4 & [h^2+ ( 16-4 h 3 )^2=4 ] or [h^2+ ( 8-4 h 3 )^2=4 ] & (25 h^2-128 h+220=0 ) or (25 h^2-64 h+28=0 ) & 25 h^2-128 h+220=0 Imaginary point aligned ) So, ( 25 h^2-64 h+28=0 ) will be considered and ( (h=2, 14 25 ) ) At (h=2, k=0 ) At (h= 14 25 , k= 48 25 ) So, ((h, k)=(2,0) ) or ( ( 14 25 , 48 25 ) )

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 AP EAMCET PYQs