Find the intersection of the line and the circle crossing the points (6,7) and (3,4). Verify this is the...

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1. Find the intersection of the line and the circle crossing the points (6,7) and (3,4). Verify this is the equation of the rectangle shown and write it in terms of x.
2. Eliminate the parameter for the following parametric equations without using Trig inverse:
x = 5cos(t) and y = 4sin(t)

SnapAndSolve AI · Accepted Answer

The equation of the line passing through points (6,7) and (3,4) is found using the slope formula: m = (7-4)/(6-3) = 1. Thus, the line equation is y = x + 1. The equation of the circle is (x - 3)^2 + (y - 4)^2 = r^2. To find the intersection, substitute y = x + 1 into the circle's equation and solve for x. Verify the intersection points lie on the rectangle.
To eliminate the parameter, use the identity cos²(t) + sin²(t) = 1. Substitute x = 5cos(t) and y = 4sin(t) into this identity: (x/5)² + (y/4)² = 1. This is the equation of an ellipse.

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Find the intersection of the line and the circle crossing the points (6,7) and (3,4). Verify this is the...

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