Question

Find the equation of the tangent on the point

30 degrees (Parametric value of theta) on the circle
${x}^{2} + {y}^{2} + 4x + 6y - 39 = 0$
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Answer 1

Given: The equation of circle x^2 + y^2 + 4x + 6y - 39 = 0

To find: The equation of the tangent on the point  30 degrees.

Solution:

• Now we have given the equation of circle:

                x^2 + y^2 + 4x + 6y – 39 = 0

• From the equation, we can say that:

                g = 2 and f = 3

                r = √(4 + 9 + 39)

                r = √52

                r = 2√3  

• We have given the angle as 30 degrees.

• So equation of tangent is:

                (x+g) cos theta + (y+f) sin theta = r

                (x+2)√3/2 + (y+3)1/2 = 2√13

• Simplifying this, we get:

                √3x + 2√3 + y + 3 = 4√13

                √3x + y + (3 + 2√3 - 4√13)  = 0

Answer:

         So the equation of the tangent is √3x + y + (3 + 2√3 - 4√13)  = 0