Help quick guys I need help on this and if you could show me how u got it or explain it to me that would be very nice thank you
1 answer:
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Answer:
The point of intersection is:
Step-by-step explanation:
We want to find the point in QI at which the line with the equation:
Intersect a circle with a radius of 3 and a center of (0, 5).
First, write the equation of a circle. The equation for a circle is given by:
Where (<em>h, k</em>) is the center and <em>r</em> is the radius.
Since our center is (0, 5), <em>h</em> = 0 and <em>k</em> = 5. The radius is 3. So, <em>r</em> = 3. Substitute:
Simplify:
At the point where the two equations intersect, its <em>x-</em>coordinate and <em>y-</em>coordinate will be the same. Therefore, we can substitute the equation of the line into the equation of the circle and solve for <em>x</em>. So:
Simplify:
Square:
Combine like terms:
Solve for <em>x: </em>
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Note that since we are looking for the point of intersection in QI, <em>x</em> should be positive. So, we can ignore the negative answer.
To find the <em>y-</em>coordinate, substitute the <em>x-</em>value back into either equation. Using the linear equation:
So, the point of intersection in QI is: