$\text{We know that the tangent at any point on a circle is perpendicular}\\
\text{to the radius at that point.}\\
\\
\text{so first we find the equation of the line joining (0,0) and (3,4)}\\
\text{and then using the slope, we find the line perperndicular to it at (3,4)}\\
\\
\text{the equation of the line passing through (0,0) and (3,4) is}\\
\\
y-0=\frac{4-0}{3-0}(x-0)$

$\Rightarrow y=\frac{4}{3}x\\
\\
\text{so the slope of radius is }m=\frac{4}{3}.\\
\\
\text{we know that the product of the perpendicular lines is }-1. \\
\\
\text{so the slope of the perpendicular line would be}=-\frac{1}{4/3}=-\frac{3}{4}\\
\\
\text{So the equation of the tangent line has slope }-\frac{3}{4} \text{ and}\\
\text{passing through (3,4). so equation of tangent line is}$

$y-4=-\frac{3}{4}(x-3)\\
\\
\Rightarrow y-4=-\frac{3}{4}x+\frac{9}{4}\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9}{4}+4\\
\\
\Rightarrow y=-\frac{3}{4}x+\frac{9+16}{4}\\
\\
\text{so the equation of tangent line is:} y=-\frac{3}{4}x+\frac{25}{4}$

5 0

4 years ago

The area of a rectangle is 42 square inches. the length is 7 inches.what is the perimeter of the rectangle?

andrew11 [14]

In order to find the perimeter, we need to have the length and the width. We are told that the area of the rectangle is 42. We will use that in the area formula, length times width, to solve for w. 42 = 7w so w = 6. The length is 7 and the width is 6. The perimeter formula for a rectangle is P = 2L + 2W. We have both the length and the width now, so we fill in accordingly. P = 2(7) + 2(6). And P=14+12. The perimeter then is 26 inches.

3 0

3 years ago

Find the equation of the line with the given properties: passes<br> through (0,-9) and (-2,-9).

irga5000 [103]

Answer:

I WRITE THE STEPS

Step-by-step explanation:

Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept. If you a point that a line passes through, and its slope, this page will show you how to find the equation of the line.

8 0

3 years ago