- x2 + y2 = 25 at (3, -4)
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Solution
Given equation of circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Next, the equation of normal is (perpendicular to the tangent and passes through origin)
- at
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Solution
Given equation of circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Next, the equation of normal is (perpendicular to the tangent and passes through origin)
- at
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Solution
Given equation of circle is
The radius of the circle is
Given point is
Now, the equation of tangent at is
Substitute and into the equation
Next, the equation of normal is (perpendicular to the tangent and passes through origin)
- at
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Solution
Given equation of circle is
The radius of the circle is
Given point is
Now, the equation of tangent at is
Substitute and into the equation
Simplify
Next, the equation of normal is (perpendicular to the tangent and passes through origin)
- at
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The radius of the circle is
Given point is
Now, the equation of tangent at is
Substitute and into the equation
Simplifying gives
Next, the equation of normal is (perpendicular to the tangent and passes through origin)
- at (3,1)
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Solution
Given equation of circle is
The center of the circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Next, the equation of normal is (perpendicular to the tangent)
The normal line passes through center , so the equation is
- at (8,6)
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Solution
Given equation of circle is
To find the center and radius, we rewrite the equation in standard form
The center of the circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Substitute , , , and into the equation
Next, the equation of normal is (perpendicular to the tangent)
The normal line passes through center , so the equation is
- at (4,-11)
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Solution
Given equation of circle is
To find the center and radius, we rewrite the equation in standard form
The center of the circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Substitute , , , and into the equation
Next, the equation of normal is (perpendicular to the tangent)
The normal line passes through center , so the equation is
- at (x, -1)
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Solution
Given equation of circle is
To find the center and radius, we rewrite the equation in standard form, then
The center of the circle is
The radius of the circle is
Given point is
Now, the equation of tangent is
Next, the equation of normal is (perpendicular to the tangent) is
The normal line passes through center , so the equation is
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