A hyperbola is the set of all points (x, y) the difference of whose distances from two distinct points called foci is constant. True False

Q: What is the equation of a circle having (10,2) and (6,-4) as endpoints of its diameter? x² + y² 16x…

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Q: The focus of the parabola y^2 = 4x is at

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Q: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: Determine the vertical traces of elliptic and parabolic cylinders in standard form.

A: Firstly the trace of a surface which is actually a cross section or the curves of intersection of a…

Q: What is the family of curves for all parabolas with axes parallel to the y-axis.

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Q: Hey, isn't a hyperbola supposed to be the to minus each other instead of plus?

A: yes you are write there is minus sign instead of plus please find below step wise solution

Q: Determine whether the statement"Every tangent line to a hyperbola intersects the hyperbola only at…

A: The tangent line at a particular point is unique as there are infinitely many points in the curve.

Q: The length of the major axis of an ellipse with foci at (-1, 2) and (3, 2) that passes through the…

A: Here we use basic defnition of major axis

Q: Which equation represents a circle with a center at (2, - 7) and a radius of 4 units?

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Q: Each of the following equations defines a geometric object in 3-space. Describe in words what the…

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Q: Which quadric surfaces have both hyperbolas and parabolas as traces?

A: Consider the given: The intersection of a three-dimensional surface and a plane is called a trace.…

Q: Is it possible for two different parabolas to have the same focus and vertex? Explain with proof.

A: Actually, there cannot be two different parabolas with same focus and vertex..

Q: O Find the equation of the parabola that has its focus at (-4, 1) and its directrix x = 0.

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Q: A searchlight uses a parabolic mirror to cast a beam of light in parallel rays where the light bulb…

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Q: Let 4x^2+3y^2+8x-6y=5 find the center and foci. Graph

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Q: Write the equation of the hyperbola of foci F1(2, −1), F2(2, 4) and focal radius difference equal to…

A: The equation of hyperbola can be obtained from the foci and the vertices or other parameters. If the…

Q: (v+5) (x+1) = 1 36 Center: 4,

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Q: The equation of the circle (x+1)²+(y+3)²=(4)² has a center and (1,3)?true or false?

A: The standers equation of a circle centered at (h,k) with radius r is given by x-h2+y-k2=r2. We…