Find the equation of the circle whose centre is at the point (1, -1) and which passes through the point (4, 3). Use centre-radius form for equation of a circle: (x- h)2 + (y - k)² = r² to express your solution %3D where centre (h, k) is (1, -1) andr= radius.

Q: What point on the parabola y=3−x2 is closest to the point ​(3​,3​)?

A: Basic differentiation is required.

Q: Find the equation of a parabola with vertex on the line y = 2X, axis parallel to the x- axis and…

A: The equation of parabola parallel to horizontal axis is  x=(y-k)2+h --------------------(1) The line…

Q: Find the parabola with equation y=x^2+bx+c that has slope of 8 when x=9 and passes through the…

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Q: Finally, determine a. The parabola passes through the point (0, 5). Substitute the values of x and y…

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Q: Find an equation for the contour of f(x, y) = 2x°y+ 8x + 15 that goes through the point (5, 2).

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Q: Find an ordered pair (x, y) that is a solution to the equation. 2x-y=4

A: For any given value of x you can find a value for y . All the ordered pairs is a solution of the…

Q: Parallel to y + 8x = 4, through (3, 4); slop- intercept form

A: The line is parallel to y+8x=4, passes through 3, 4

Q: How far is the center equation 10x^2 -y^2 -5y -11 to its focus?

A: Note: It is assumed that the equation, 10x2-y2-5y-11 is 10x2-y2-5y-11=0.   The conics are generated…

Q: Find the equation of the line tangent to the circle x + y + 6x - 2y - 15 = 0 at the point (1,-2).

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Q: Find the point(s) of intersection of the line y=7x-42 and the circle with equation x2+y2-4x+6y=12.

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Q: Find the equation of a line tangent to the circle x2 +y2 – 4x + 2y - 31 = 0 at the point (2,5). Draw…

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Q: The point that is 2 units to the left of the y-axis and 4 units above the x-axis has coordinates (,.

A: A point which is a units to the left of y-axis and b units above the x-axis is given by the…

Q: What is the equation of the parabola which has vertex (1,2) and y-intercept y = 1?

A: See the details solution in below

Q: The circle given by the equation x² + y² + ax + by + c = 0 passes through the points (-2, 0), (1,…

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Q: Find the equation of the parabola and put it in the form f(x)= ax^2 +bx+c  Given:  vertex: (7, -4)…

A: Explained below

Q: 2. f(x) = 2 - 5x + 2x Sketch: Opens: Vertex: Equation for Axis of Symmetry:

A: The quadratic function is f(x)=2-5x+2x2 Let the function of the form f(x)=ax2+bx+c, if a > 0 then…

Q: Find the equation that is perpendicular to y = 2x – 1 and passes through the point (2,3). What is…

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Q: find (y" ) for the following equation 3x²-2y'-y=6 at point (2,1)

A: Take the first derivative of the whole term than find y' at given point after this calculate second…

Q: Find the points of intersection of the curves y = 5x2 - 3x - 2 and y = 2x - 1.

A: We have the equation of curves as y=5x2-3x-2            ⋯⋯1y=2x-1                      ⋯⋯2

Q: Find the equation of the plane perpendicular to the y-axis and passing through the point (3,2,-2)

A:

Q: A hawk flying at 18 m/s at an altitude of 190 m accidentally drops its prey. The parabolic…

A: Given that: y=190-x254 Let,  y=0190-x254=0190=x254x=101.29So  the  distance  travelled  is  the  one…

Q: Find the equation of the parabola with vertex (−3,1)(−3,1) and yy-intercept 22(or (0,2)(0,2)).

A: topic - equation of a parabola

Q: Find the equations of the curve for which y" = 6x2 and which passes through the points (0,2) and…

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Q: Find an equation for the contour of f(x, y) = 2a²y + 6x + 15 that goes through the point (4, 1).…

A: A contour line of the quadric surface is the curve of intersection of the quadric surface with the…

Q: Find the equation that is perpendicular to y = x +3 and passes through the point (-3, -4). %3D Oy =…

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Q: What point on the parabola y=(6−x)2 is closest to the point (6​,6​)?

A:

Q: Find equations for the osculating circles of the parabola y=0.5x2 at the points (0,0) and (-1,1/2).

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Q: 21. Write the standard equation of a circle with center (-4, 0) and radius 3. (x- 4)2 + y2 = 3 (x+…

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Q: Find the point(s) of intersection of the parabola with equation y = x2 - 5x + 4 and the line with…

A: Given equations are,

Q: Q2. What is the equation of the circle whose center is (3,4) and tangent with (x-axis)

A: 2. Equation of circle with center at (a, b) and radius r is as follows. (x-a)2+(y-b)2=r2. Center of…

Q: (i) Find the equation of the circle passing through (0,0) and making intercepts 4,3 on X-axis and…

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Q: Find the equation of the plane perpendicular to the x-axis and passing through the point (-2,3,2)

A: Find the equation of the plane perpendicular to the x-axis and passing through the point (-2,3,2)

Q: Write the equation in standard form for the circle with radius 4 centered at the origin. x² + y² =…

A: Use the standard formula for the equation of circle when centre and radius are given.

Q: What is the equation of a circle with center (-3, 5) that passes through the point (1, 5)? 2 OA…

A: To find the equation of the circle having center (-3, 5) and passing through the point (1, 5)

Q: find the general equation of the parabola with horizontal axis which crosses the x-axis at x=2 and…

A:

Q: A hawk flying at 16 m/s at an altitude of 170 m accidentally drops its prey. The parabolic…

A:

Q: Find the points of intersection of the parabola with equation 2x + y² + 4y – 2 = 0 and the line…

A: Here we find the intersecting point of parabola and the line.

Q: Find the equation of perpendicular bisector of the line passing through points (2,-5) to the point…

A: perpendicular bisector passes through mid point of the points and has perpendicular slope to the…

Q: The y coordinate of (-2, 4) is what?

A: Given, -2,4 To find the y - coordinate of the point.

Q: Find the equations of the curve for which y" = 6x2  and which passes through the points (0,2) and…

A: We have to find equation of curve, With differential equation y" = 6x2  which passes through the…

Q: What point on the parabola y = 6 – x is closest to the point (6,6)?

A:

Q: Find an equation of the paranola in standard form: with the vertex at V (2,-4) and directrix y= -5

A: Find an equation of the parabola in standard form: with the vertex at V (2,-4) and directrix y= -5

Q: Find the equation of the parabola with directrix y = 3, axis x = 0, and latus rectum 4

A: Given: Equation of directrix:y=3……1Equation of axis:x=0……2Length of latus rectum:4……3

Q: Find the equation of the parabola with directrix x + 2 = 0, axis y = 4, and latus rectum 4.

A:

Q: DD,- D,-+2y)?

A: Given that, Dx2r-1Dx-Dyz=x+2y2 To show that : the rank of equation is uniform . From the given…

Q: find the equation of the line passing through the point (-2,1) and perpendicular to the line with…

A: From the given information, it is observed that a line passes through the point (–2,1) and…

Q: Find the equation of the line tangent to (a) The parabola z = 2x² - 3y², y = 1 at the point (-2,1,5)…

A: Given: we have to find equation of tangent lines   equation of tangent line : y-y1=m(x-x1)