Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202125 Aug 2021Evening ShiftMathematicsCircleActual

The equations of the tangent to the circle 5 x^2+5 y^2=1 parallel to the line 3 x+4 y=1 are

Options

  1. A3 x+4 y= 2 5
  2. B3 x+4 y= 5
  3. C6 x+8 y= 5
  4. D3 x+4 y= 3 5

Correct answer

B. 3 x+4 y= 5

Step-by-step solution

Given, equation of circle is 5 x^2+5 y^2=1 aligned & x^2+y^2=(1 / 5 )^2 & Centre =(0,0) and radius =1 / 5 aligned Given, line is 3x + 4y = 1 Slope (m)= -3 4 Since, we know that tangents to the circle x^2+y^2=a^2 in the slope form is given by y=m x a 1+m^2 ...(i) Since, required line is parallel to given line, hence it will have same slope and radius = 1 5 From Eq. (i), we get aligned & y= -3 4 x 1 5 1+ ( -3 4 )^2 = -3 4 x 1 5 25 16 & y= -3 x 4 1 5 5 4 4 y=-3 x 5 & 3 x+4 y= 5 aligned

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