13. The sum of the measures of angle Mand angle Ris 90°.
1 answer:
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Answer:
y = - (x - 1)² + 2
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
= | y - 6 |
Square both sides
(x - 1)² + (y + 2)² = (y - 6)² ( expand the factors in y )
(x - 1)² + y² + 4y + 4 = y² - 12y + 36 ( subtract y² - 12y from both sides )
(x - 1)² + 16y + 4 = 36 ( subtract 4 from both sides )
(x - 1)² + 16y = 32 ← subtract (x - 1)² from both sides )
16y = - (x - 1)² + 32 ( divide all terms by 16 )
y = - (x - 1)² + 2
This is an isosceles triangle. The angles at the base are congruent (they have the same measures).
Look at the picture.
We know: The sum of the measures of angles in a triangle is equal 180°.
Therefore we have the equation:
<em>combine like terms</em>
<em>subtract 5 from both sides</em>
<em>divide both sides by 7</em>
