gaokao 2019 Q15

gaokao · China · national-III-science 5 marks Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

Let $F _ { 1 } , F _ { 2 }$ be the two foci of the ellipse $C : \frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 20 } = 1$ , and $M$ be a point on $C$ in the first quadrant. If $\triangle M F _ { 1 } F _ { 2 }$ is an isosceles triangle, then the coordinates of $M$ are \_\_\_\_\_\_.

$( 3 , \sqrt { 15 } )$

Let $F _ { 1 } , F _ { 2 }$ be the two foci of the ellipse $C : \frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 20 } = 1$ , and $M$ be a point on $C$ in the first quadrant. If $\triangle M F _ { 1 } F _ { 2 }$ is an isosceles triangle, then the coordinates of $M$ are \_\_\_\_\_\_.

Paper Questions

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