The equations of the tangent to the curve x^2 + y^2 = 10 , where the tangent is parallel to the line 2x + y - 1 = 0 , are

Step-by-step solution

The given curve is a circle x^2 + y^2 = 10 with center (0,0) and radius r = 10 . The tangent is parallel to the line 2x + y - 1 = 0 . Let the equation of the tangent be 2x + y + c = 0 . The perpendicular distance from the center of the circle to the tangent is equal to its radius. |2(0) + (0) + c| 2^2 + 1^2 = 10 |c| 5 = 10 |c| = 50 = 5 2 c = 5 2 The equations of the tangents are 2x + y = 5 2 . Answer: 2x + y = 5 2