Question

80. Find the equation of the tangents to
the circle x² + y2 - 4x-6y +3=0 which
makes an angle 45° with X-axis. (*)​

Answer 1

Answer:

Assume that the line is y=x+c ——(1) which a line making an angle of 45° with the x-axis. The given circle: x²+y²-4x-6y+3=0 ——(2). Solve (1) & (2) simultaneously and arrive at the condition: c² - 2c - 19=0 which would imply that there two possible values of c viz. 1±2√5. In other words, two such lines are possible: y = x + (1 ± 2√5)

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