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Is there a point P on the parabola's axis of symmetry such that ∠APB = 2∠AQB and there is only one s
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The parabola y = a (x + 2) ^ 2 + c intersects the X axis at A and B, and intersects the Y axis at C. We know that point A (1,0), OB = OC.
(1) Write the analytical expression of the parabola
(2) Point Q is a point on the straight line y = x4. Is there a point P on the parabola's axis of symmetry such that ∠APB = 2∠AQB and there is only one such point Q? If present, the coordinates of the point P are requested. If not, please explain why.
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distance((x0,y0),(x1,y1))=sqrt((x1x0)^2+(y1y0)^2) then repeat:
write and solve the bold equation in my post
distance(P,B)=distance(P,Q) P=(2,y) Q=(t4,t) then y=(2t^2+4t+3)/(2t)
https://help.geogebra.org/t...
Correct the title

(2) Point Q is a point on the straight line y = x4. Is there a point P on the parabola's axis of symmetry such that ∠APB = 2∠AQB and there is only one such point Q? If it exists, find the coordinates of point P. If not, please explain why.
Is there a point P on the parabola's axis of symmetry such that ∠APB = 2∠AQB and there is only one such point P?
There is indeed a P point on the parabola's axis of symmetry, and even an infinity by moving the Q point on the right yx4,
which verifies the relationship 'APB' to 2'AQB.
Let's trace the mediator of the AQ segment, which cuts the axis of symmetry to a P point.
Let's build the P center circle through the Q, A and B points, the APB and AQB angles
check the relationship with ABP and AQB angles (because ABP is the angle in the centre and AQB underlies the same AB arc).
The coordinates of point P are that of the center of the circle.
Hi,
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