Given that P is the point on the ellipse X225 + Y29 = 1, Q and R are the points on the circle (x + 4) 2 + y2 = 14 and (x − 4) 2 + y2 = 14 respectively, then the minimum value of | PQ | + | PR | is () A. 89B. 85C. 10D. 9 | Math enthusiast | Mathematical art

Given that P is the point on the ellipse X225 + Y29 = 1, Q and R are the points on the circle (x + 4) 2 + y2 = 14 and (x − 4) 2 + y2 = 14 respectively, then the minimum value of | PQ | + | PR | is () A. 89B. 85C. 10D. 9

It can be seen from the title that the centers of the two circles (x + 4) 2 + y2 = 14 and (x − 4) 2 + y2 = 14 are exactly the two focal points F1 (- 4, 0) and F2 (4, 0) of the ellipse. From the definition of the ellipse, we know that | Pf1 | + | PF2 | = 2A = 10, so we can get that the minimum value of | PQ | + | PR | = | Pf1 | + | PF2 | - 2R = 10 − 2 × 12 = 9

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