The line 3 x-y+k=0 touches the circle x2+y2+4 x-6 y+3=0 . If k1, k2(k1

Question

The line 3 x-y+k=0 touches the circle x2+y2+4 x-6 y+3=0 . If k1, k2(k1< k2) are the two values of k, then the equation of the chord of contact of the point (k1, k2) with respect to the given circle is (A) 19 x+y-18=0 (B) x+19 y-3=0 (C) x+16 y-56=0 (D) 20 x+18 y-7=0

Tardigrade Admin · Accepted Answer

Line 3 x-y+k=0 touches the circle x2+y2+4 x-6 y+3=0 having Centre (-2,3), r=√4+9-3=√10 ∵ r=|(-6-3+k/√10)| <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/39e12ee92d3af0cc4bdd844c1631e541-.png" /> 10=|-9+k| ⇒ ± 10=k-9 ∴ k =-1,19 k1 =-1, k2=19 Equation of chord of contact of (-1,19) to the circle -x+19 y+2(x-1)-3(y+19)+3=0 ⇒ x+16 y-56=0

Q. The line $3 x - y + k = 0$ touches the circle $x^{2} + y^{2} + 4 x - 6 y + 3 = 0.$ If $k_{1}, k_{2} (k_{1} < k_{2})$ are the two values of $k$ , then the equation of the chord of contact of the point $(k_{1}, k_{2})$ with respect to the given circle is

$19 x + y - 18 = 0$

$x + 19 y - 3 = 0$

$x + 16 y - 56 = 0$

$20 x + 18 y - 7 = 0$

Q. The line 3x−y+k=0 touches the circle x2+y2+4x−6y+3=0. If k1​,k2​(k1​<k2​) are the two values of k, then the equation of the chord of contact of the point (k1​,k2​) with respect to the given circle is

19x+y−18=0

x+19y−3=0

x+16y−56=0

20x+18y−7=0

Q. The line $3 x - y + k = 0$ touches the circle $x^{2} + y^{2} + 4 x - 6 y + 3 = 0.$ If $k_{1}, k_{2} (k_{1} < k_{2})$ are the two values of $k$ , then the equation of the chord of contact of the point $(k_{1}, k_{2})$ with respect to the given circle is

$19 x + y - 18 = 0$

$x + 19 y - 3 = 0$

$x + 16 y - 56 = 0$

$20 x + 18 y - 7 = 0$