<![CDATA[Is there a point P on the parabola's axis of symmetry such that ∠APB = 2∠AQB and there is only one s]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s
Mon, 06 Jan 2020 15:56:31 +0000Sun, 05 Jan 2020 02:39:47 +0000Zend_Feed<![CDATA[Correct the title ---------------------------- (2) Point Q is a point on the straight line y = -x-4. 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.]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273258
Sun, 05 Jan 2020 06:24:00 +0000<![CDATA[ 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?or 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?]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273266
Sun, 05 Jan 2020 11:27:28 +0000<![CDATA[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 y-x-4, 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.]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273268
Sun, 05 Jan 2020 12:08:20 +0000<![CDATA[point Q,no mistake in the title,Point Q is a point on the straight line y = -x-4.and point P on the parabola's axis of symmetry.]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273272
Sun, 05 Jan 2020 12:26:08 +0000<![CDATA[You may have got the parabola formula wrong. The parabola is y = - x ^ 2-4x-3, not y = - x ^ 2-4x + 2 As you did, circle P has at least two intersections with line y = - x-4.]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273276
Sun, 05 Jan 2020 13:25:13 +0000<![CDATA[Hi, ...]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273278
Sun, 05 Jan 2020 14:30:59 +0000<![CDATA[Your diagram should be correct and meet the requirements of all topics, but how can the coordinates of point P be calculated? Thank you]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273282
Sun, 05 Jan 2020 15:49:49 +0000<![CDATA[mi pregunta es si es el punto P el que es unico para cada Q. es decir el punto Q es cualquier punto del eje y el punto P es unico (en realidad hay dos considerando AQB<180º) para cada Q supón t=y(Q) entonces y(P)=(2t^2+4t+3)/(2t)]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273284
Sun, 05 Jan 2020 22:14:59 +0000<![CDATA[en este diagrama Q es unico para P si distancia(P,B)=distancia(P,g) es fácil entonces averiguar P]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273288
Sun, 05 Jan 2020 22:43:12 +0000<![CDATA[The meaning of the question is that point P is unique. There is no limit to whether point P is unique, as long as the point P is on the axis of symmetry, the point Q is on the line y = -x-4, and the two angles mentioned in the title are two Double the relationship.]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273290
Sun, 05 Jan 2020 22:53:42 +0000<![CDATA[The graph should be correct and meet the requirements of the problem. So how to calculate the coordinates of P? Or help me think about how to calculate the coordinates of point P, thank you]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273292
Sun, 05 Jan 2020 23:01:02 +0000<![CDATA[write and solve the bold equation in my post distance(P,B)=distance(P,Q) P=(-2,y) Q=(-t-4,t) then y=(2t^2+4t+3)/(2t) see my above post]]>
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Sun, 05 Jan 2020 23:43:08 +0000<![CDATA[Thank you, but I would like to ask how did the function "y = (2t ^ 2 + 4t + 3) / (2t)" come from in your answer? This function is not in the title?]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273298
Mon, 06 Jan 2020 01:20:49 +0000<![CDATA[distance((x0,y0),(x1,y1))=sqrt((x1-x0)^2+(y1-y0)^2) then repeat: write and solve the bold equation in my post distance(P,B)=distance(P,Q) P=(-2,y) Q=(-t-4,t) then y=(2t^2+4t+3)/(2t) https://help.geogebra.org/t...]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273340
Mon, 06 Jan 2020 10:44:33 +0000<![CDATA[Just for the fun ... The coordinates of the 3 points are : P(-2,y) , B(-1,0), Q(-t-4,t) Distance PQ = sqrt(-2-(-t-4))^2 + (y-t)^2) = sqrt((t+2)^2 + (y-t)^2) Distance PB = sqrt((-2+1)^2 + (y-0)^2)=sqrt(y^2+1) Distance PQ = Distance PB ==> Solve sqrt(y^2+1) = sqrt((t+2)^2 + (y-t)^2) y^2+1 = ((t+2)^2 + (y-t)^2 y^2+1 = t^2+2t+4+y^2-2yt+t^2 Then ==> y=(2t^2+2t+3)/2t ]]>
https://help.geogebra.org/topic/is-there-a-point-p-on-the-parabolas-axis-of-symmetry-such-that-apb-2aqb-and-there-is-only-one-s#comment-273358
Mon, 06 Jan 2020 15:56:32 +0000