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Serggg [28]
3 years ago
7

Ind the equation of the tangent line to 9x^2+16y^2=52 through (2, -1)

Mathematics
1 answer:
EastWind [94]3 years ago
6 0
Here are the steps.

In order to get the answer, first we need to get the x and y value of the center of the circle by using the equation of a circle (x^2 + y^2 = r^2)

<span>The center is (-9, -4)</span>

Once you get the center point, find the equation of the line (in a form of a radius) from the center point to point (2, -1). Get the slope.

The slope from center to point (2, -1) is 11/3

Finally, get the negative reciprocal of the slope from the previous step and form the equation using slope-intercept form ( y=mx + b). Then, that's the equation of the tangent line.

The slope of the tangent line is -3/11
The equation is y = -3/11x - 5/11

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Compute and compare the side lengths of the two figures. Does this support an argument claiming that they are congruent? What el
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We compute for the side lengths using the distance formula √[(x₂-x₁)²+(y₂-y₁)²].

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CD = √[(-3--5)²+(4-1)²] = √13
C'D' = √[(-5--7)²+(0--3)²] = √13

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D'A' = √[(-7--9)²+(-3-0)²] = √13

The two polygons are squares with the same side lengths. 

But this is not enough information to support the argument that the two figures are congruent. In order for the two to be congruent, they must satisfy all conditions: 
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2. All the corresponding sides have equal length.
3. All the corresponding interior angles have the same measurements.

The third condition was not proven.
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hope this helps

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