The circle is closed and the graph is shaded to the right also there’s a negative on the x, you have to get rid of it first by dividing by -1 and then you switch direction of the less than or equal to greater than or equal because you divided by negative
The tangent line to <em>y</em> = <em>f(x)</em> at a point (<em>a</em>, <em>f(a)</em> ) has slope d<em>y</em>/d<em>x</em> at <em>x</em> = <em>a</em>. So first compute the derivative:
<em>y</em> = <em>x</em>² - 9<em>x</em> → d<em>y</em>/d<em>x</em> = 2<em>x</em> - 9
When <em>x</em> = 4, the function takes on a value of
<em>y</em> = 4² - 9•4 = -20
and the derivative is
d<em>y</em>/d<em>x</em> (4) = 2•4 - 9 = -1
Then use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-20) = -1 (<em>x</em> - 4)
<em>y</em> + 20 = -<em>x</em> + 4
<em>y</em> = -<em>x</em> - 24
The normal line is perpendicular to the tangent, so its slope is -1/(-1) = 1. It passes through the same point, so its equation is
<em>y</em> - (-20) = 1 (<em>x</em> - 4)
<em>y</em> + 20 = <em>x</em> - 4
<em>y</em> = <em>x</em> - 24
<h3>
Answer: A) parabola</h3>
Some degenerate parabola cases form a single straight line, while other cases form one pair of parallel lines.
A degenerate hyperbola forms two lines that intersect at the vertex of the cone. We can rule out choice B.
A degenerate circle is a single point, so we can rule out choice C.
A degenerate ellipse is also a single point. Any circle is an ellipse (but not the other way around). We can rule out choice D.
Answer:
(9,-2)
Step-by-step explanation:
9 is on x and y is -2
(x,y) is the rule so here ya go hope it helps :)
