A circle passes through point P (2, - 1) and is tangent to the straight line X-Y = 1. The center of the circle is on the straight line y = - 2x | Math enthusiast | Mathematical art

A circle passes through point P (2, - 1) and is tangent to the straight line X-Y = 1. The center of the circle is on the straight line y = - 2x

Let the coordinates of the center of a circle be o (x, - 2x), then the distance from O to the point (2, - 1) is equal to the distance from O to the straight line X-Y = 1. The solutions of the equations are as follows: (x-1) ^ 2 + (Y + 2) ^ 2 = 2 or (X-9) ^ 2 + (y + 18) ^ 2 = 338

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1. Given a circle passing through point P (2, - 1), the center of the circle is on L1: y + 2x = 0 and tangent to the line L2: x-y-1 = 0, the equation of the circle is obtained
2. Given that the circle passes through the point P (2, - 1) and is tangent to the straight line X-Y = 1, and its center is on the straight line y = - 2x, the equation of the circle is obtained
3. Find out the equation of the circle which passes through a (2, - 1) and is tangent to the line x + y = 1, and the center of the circle is on the line y = - 2x. (I) find out the standard equation of the circle; (II) find out the chord length AB of the intersection of the circle in (I) and the line 3x + 4Y = 0
4. When a circle passes through a (2,1) point and is tangent to a straight line X-Y = 0, and the center of the circle is on 2x-y = 0, the standard equation of the circle is obtained
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6. As shown in the figure, in O, the chord AB = AC = 10, the chord ad intersects BC with E, AE = 4, and the length of ad is calculated
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8. It is known that: as shown in the figure, AB is the diameter of ⊙ o, AC is the chord, CD ⊥ AB at D. if AE = AC, be intersects ⊙ o at point F, CF and de are connected
9. As shown in the figure, AB and AC are the chords of ⊙ o, ad ⊥ BC at D, intersection of ⊙ o at F, AE and diameter of ⊙ O. what is the relationship between the two chords be and the size of CF? Explain the reason
10. If ad ^ 2 = AE * AC, CD = CB
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