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If the line hx+KY=1/a touches the circle x²+y²=a² then the locus of (h,k) is circle of radius 1)1/a 2)a² 3)a 4)1/a²

If the line hx+KY=1/a touches the circle x²+y²=a² then the locus of (h,k) is circle of radius
1)1/a
2)a²
3)a
4)1/a²

Grade:11

1 Answers

Shukant Pal
25 Points
3 years ago
In this question, you just need to apply the condition of tangency of a line w.r.t to a circle, .i.e, perpendicular distance of the line from the center of the circle is equal to its radius.
 
The equation of the line is – hx + ky – 1/a = 0 and C(0, 0) and radius of circle is ‘a’.
 
Thus, |[0*h + 0*k – 1/a] / sqrt(h2 + k2)]| = a.
 
Solving this you will get – sqrt(h2 + k2) = 1/a2 or radius of circle is 4) 1/a2

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