The locus of the midpoints of the chords drawn from the point M(1,8) to the circle x2+y2-6 x-4 y-11=0, is a circle whose radius, is

Question

The locus of the midpoints of the chords drawn from the point M(1,8) to the circle x2+y2-6 x-4 y-11=0, is a circle whose radius, is (A) 2 √2 (B) 3 (C) √10 (D) 4 √2

Tardigrade Admin · Accepted Answer

Clearly, mC P × mA B=-1 ⇒(( k -2/ h -3)) ×(( k -8/ h -1))=-1 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/3eb6e46d712b921cb1eea51f0e945ae2-.png" /> ∴ Locus of (h, k) is (x-1)(x-3)+(y-2)(y-8)=0 i.e., x2+y2-4 x-10 y+19=0. Point P moves on circle with CM as diameter ∴ Radius =( CM /2)=(√22+62/2) =√1+9=√10 .

Q. The locus of the midpoints of the chords drawn from the point $M (1, 8)$ to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ , is a circle whose radius, is

$22$

3

$10$

$42$

Q. The locus of the midpoints of the chords drawn from the point M(1,8) to the circle x2+y2−6x−4y−11=0, is a circle whose radius, is

22​

3

10​

42​

Clearly, mCP​×mAB​=−1 ⇒(h−3k−2​)×(h−1k−8​)=−1 ∴ Locus of (h,k) is (x−1)(x−3)+(y−2)(y−8)=0 i.e., x2+y2−4x−10y+19=0. Point P moves on circle with CM as diameter ∴ Radius =2CM​=222+62​​ =1+9​=10​.

Q. The locus of the midpoints of the chords drawn from the point $M (1, 8)$ to the circle $x^{2} + y^{2} - 6 x - 4 y - 11 = 0$ , is a circle whose radius, is

$22$

$10$

$42$