Question

Find the points on the curve x2 + y2 -2x-3 = 0 where the tangent is parallel to the x- axis

Answer 1

Answer:

(1,2) and (1,-2) are the two points where the tangent is parallel to the x-axis.

Step-by-step explanation:

The equation of the curve can be reduced to:

(x-1)^2 + y^2 = 4

Therefore, the centre is (1,0) on the x axis

and, the radius is 2 units.

Now, if we add and subtract 2 to the y coordinates of the centre we get

(1,2) and (1,-2) are the two points where the tangent is parallel to the x-axis.

y=2 and y=-2 are the two equations of tangents to the circle and also parallel to axis and equation of the line x=1  represents the diameter perpendicular to the x axis.