To calculate:The equation for the circle and line in the given figure.
The equation for the circle and line in the figure are and respectively.
The point lying on the tangent to the circle with center
For a given circle with center and radius the equation is given as:
This is referred to as the Standard form for the equation of a given circle.
The distance between two points say and is given as:
Slope m of the line passing through two points in general say and is:
Slope-intercept equation for a given line which has slope as and −intercept as is:
Two-intercept equation for a given line which has -intercept as and −intercept as is:
When two lines are perpendicular then the product of their slopes is zero that is
When two lines are parallel then their slope are equal that is
From the given figure it is clear that center of the circle is
Recall for a given circle with center and radius the equation is given as:
Therefore, replacing the values we get:
Now to find radius which is the distance from the center to the point
Recall, the distance between two points say and is given as:
Before applying distance formula the following must be known:
Put this value in
Therefore, the required equation for circle is:
Hence, the equation for the given circle is
Now for the equation of line:
Recall, slope m of the line passing through two points in general say and is:
As it is known:
Therefore, slope of radius for above values is:
Now as the tangent is perpendicular to the circle, therefore the product of their slopes is
Slope of line is
And it passes through that is
Put these values in the general equation for the line which is
Now put and in to get:
Thus, required equation of line is
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