If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle at the point is , then is equal to
Step 1: Draw a schematic diagram diagram with the given date in the question
From the given equation of circle , the centre is at and its radius is , then
Step 2: Find the equation of normal,
From point and , the equation of normal is
When , then
Then the point of intersection with the x-axis, that is point
Step 3: Find the equation of tangent,
we know that the product of slopes of normal and tangent is equal to , as both are perpendicular to each other.
From equation (i) the slope of normal, ,
we know , then ,
Using the slope and a point , the equation of tangent can be written as
When , then
Then the point of intersection with the x-axis, that is point
Step 4: Calculate the Area PQR,
Area of triangle
Using the figure, Height , and
Therefore, the area , then
Hence, .