12: A tangent to the circle x² + y? = 5 at the point (1,2) and th circle x? + y² – 8x + 6y + 20 - A) Touches B) Cuts at real points C) Cuts at imaginary points

Q: Find the image of the circle x2 + y² = 4 under a dilation of factor 2 from the x-axis followed by a…

A: The dilation of a curve indicates the expansion or contraction of the curve. If a curve is dilated…

Q: nd the condit. on if the circle whose equation a x² + y² + c² = 2ax = 0 and x² + y² + c² = 2b y = 0…

A: The two circles are x2+y2+c2=2ax=0 and x2+y2+c2=2by=0.centers:C1(a,0),C2(0,b)radii:r1=a2=c2,r2=b2-c2

Q: Form the diffrential equation of the family of circle having a centre on y-axis and radius 3 units.

A: the objective is to find the differential equation of the family of circles having centre on y axis…

Q: Find the distance from the point (5,8) to the circle x2 + Y2 + 2x + 6y + 3 = 0

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Q: Evaluate ∫ C ( 2 + x^2 y ) d s , where C is the upper half of the unit circle.

A: We have to evaluate the line integral: ∫C2+x2yds where C is the upper half of the unit circle.

Q: Find ∫C (2z + 9) / (z2 + 2z - 3) where C is the circle |z - 2| = 3.

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Q: The distance of the line 7x + y –5 = 0 from the origin is?

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Q: 2. The circle, if the center of the circle of radius 3 lies on the line x + 2y = 4 and it is tangent…

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Q: Is the point (-15, 15) on the circle defined by (x+15)+(y-15) = 100? Yes No X Ś

A: To determine whether the given point lies on the circle or not.

Q: Q2) Find the distance between the line y= - (x+2 ) & the center of the circle y + x – 4(x+ y )= 9

A: The center of the circle x2+y2-2ax-2by+c=0 is a, b Therefore, the center of the given circle…

Q: ,draw the circle given by the equation (x+4)² + (y –6)² = 16. THIN BLACK 13- 12- 11+ 10 9- 8- -거 6-…

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Q: Concentric with the circle x ^ 2 + y ^ 2 - 4x + 6y - 17 = 0 and 3x - 4y + 7 = 0 equation of the…

A: Solution:- x2+y2-4x+6y-17=0 x2-4x+6y+y2=17 x2-4x+4+6y+y2+9=17+4+9 x-22+y+32=30 Center of circle (2,…

Q: 8. Is the point (2, –7) on the circle defined by (x + 6) + (y + 1) = 100?

A: Given the equation of a circle, x+62+(y+1)2=100                   ...(1)

Q: 5. Show that the sum of the intercepts of the tangent to the parabola (Art. 129), x+y=a¹, is equal…

A: We need to prove given theorem.

Q: Find the cоттоn points of the circles (x + 1)² + (y – 1)² = 5 and x² + y? = 1.

A: Common points of the circles simply means the point of intersection of the given circles.

Q: There are exactly two values of y that make the points A = (0, 1), B = (4, – 10) and C = (-15, y)…

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Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…

Q: What are the four main end points to the circle x2+y2-10x+8y+25=0 (show work)

A: Question is solved.

Q: To y=x²-12x + 20 Parabola Wite the intersection point of the tanpent lines drawn from (2,0) and…

A: Consider the given parabola and find the derivative of the parabola.…

Q: How many common points does the parabola y=x2-2x-2 have with the straight line a) y=2x-6; b) x-2y=4?

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Q: 3.2. (a) Use the lines through the point (1, 1) to describe all the points on the circle 1 + y? = 2…

A: We can draw a line ML passing through the points P(1,1) and M(x ,y). Let the slope of L be m. We can…