Can someone help with at least one of these?

Question

Create an equation of a circle and calculate the circumference of this circle and area if the center of the circle is located at the point (3; 0) and the circle passes through the point (7; 0).

Find the lines 𝑦 = 4𝑥2 − 16 and 𝑦 = 12𝑥 − 24 intersection points. Draw lines and their intersection points in the figure.

Find the circle (𝑥 − 4)2 + 𝑦2 = 5 the equation of the tangent drawn at point (6; 1) and make drawing.

Answer 1

meone help with at least one of these?

Create an equation of a circle and calculate the circumference of this circle and area if the center of the circle is located at the point (3; 0) and the circle passes through the point (7; 0).

Find the lines 𝑦 = 4𝑥2 − 16 and 𝑦 = 12𝑥 − 24 intersection points. Draw lines and their intersection points in the figure.

Find the circle (𝑥 − 4)2 + 𝑦2 = 5 the equation of the tangent drawn at point (6; 1) and make drawing.

first question. radius is 4, circumference is 8π, area 16π, equation (x-3)²+y²=16

second, set y=y have 4x²-12x+8=0,,,(2x-4)(2x-2)=0,,,,solutions x=2 and x=1

at x=2 y=0 (2,0) and at x=1 y=-12 (1,-12)

third, notice (6,1) is √5 from center and radius is √5. So (6,1) is on circle.

the slope of the center to (6,1) point is (1-0)/(6-4)=1/2

tangent at (6,1) point must have slope of -2 to be perpendicular to radius line

tangent line is -2=(y-1)/(x-6),,,,y=(-2)x+13