The equations of the tangents to the circle x2-y2-6 x-4 y-12 which are parallel to the straight line 4 x-3 y-5-0- areA- 4 x-3 y-19-0-4 x-3 y-31-0B- 3 x-4 y-19-0-3 x-4 y-31-0C- 3 x-4 y-19-0-3 x-4 y-31-0D- 4 x-3 y-19-0-4 x-3 y-31-0

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Equation of Tangent in Slope Form

The equations...

Question

The equations of the tangents to the circle $x^{2} + y^{2} - 6 x + 4 y = 12$ which are parallel to the straight line 4x + 3y + 5 = 0, are

3x - 4y - 19 = 0, 3x - 4y + 31 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4x + 3y - 19 = 0, 4x + 3y + 31 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4x + 3y + 19 = 0, 4x + 3y - 31 = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3x - 4y + 19 = 0, 3x - 4y + 31 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 4x + 3y + 19 = 0, 4x + 3y - 31 = 0
Let equation of tangent be 4x + 3y + k = 0, then $\sqrt{9 + 4 + 12} = ∣ ∣ ∣ \frac{4 (3) + 3 (- 2) + k}{\sqrt{16 + 9}} ∣ ∣ ∣$
$\Rightarrow 6 + k = \pm 25 \Rightarrow k = 19 a n d - 31.$
Hence the tangents are 4x + 3y + 19 = 0 and 4x + 3y - 31 = 0.

Suggest Corrections

119

Similar questions

Q. The area of the parallelogram formed by the lines

3 x - 4 y + 1 = 0, 3 x - 4 y + 3 = 0, 4 x - 3 y - 1 = 0

and

4 x - 3 y - 2 = 0,

Q. The equations of the tangents to the circle

x^{2} + y^{2}

- 4x - 6y - 12 = 0 and parallel to 4x - 3y = 1 are

Q. The equation of the tangents to the circle

x^{2} + y^{2} + 6 x + 6 y + 2 = 0

, which is parallel to

3 x + 4 y + 8 = 0

are

Q. Prove that the area of the parallelogram formed by the lines 3x − 4y + a = 0, 3x − 4y + 3a = 0, 4x − 3y − a = 0 and 4x − 3y − 2a = 0 is

\frac{2}{7} a^{2}

sq. units.

Find the equation of circle circumscribing the quadrilateral formed by four lines $3 x + 4 y - 5 = 0$ , $4 x - 3 y - 5 = 0$ , $3 x + 4 y + 5 = 0$ and $4 x - 3 y + 5 = 0$

Join BYJU'S Learning Program

The equations of the tangents to the circle x2+y2−6x+4y=12 which are parallel to the straight line 4x + 3y + 5 = 0, are

The correct option is C 4x + 3y + 19 = 0, 4x + 3y - 31 = 0Let equation of tangent be 4x + 3y + k = 0, then √9+4+12=∣∣∣4(3)+3(−2)+k√16+9∣∣∣ ⇒6+k=±25⇒k=19and−31. Hence the tangents are 4x + 3y + 19 = 0 and 4x + 3y - 31 = 0.

The equations of the tangents to the circle $x^{2} + y^{2} - 6 x + 4 y = 12$ which are parallel to the straight line 4x + 3y + 5 = 0, are