37. Two circles are said to be orthogonal if the radius drawn from one of the circles to a point of intersection is perpendicular, at that point, to the radius drawn from the other circle. Prove that if two orthogonal circles have two points of intersection, the radii are perpendicular at both points of intersection.

Q: If the circle x2+y2+ax+by-12=0 has the centre  at (2,3) then find a , b and radius

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Q: Let the triangle ABC and A ', B', C ', the intersections of the tangents to its circumscribed circle…

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Q: A circle passes through the point (6, 2). If segments of the straight lines x + y = 6 and x + 2y = 4…

A: We can find the radius as below.

Q: Show that the equation of a circle passing through the origin and having intercepts a and b on real…

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Q: Find all points with coordinates of the form (a, a) that are a distance 3 from P(-2, 1).

A: Given: P(-2,1) and distance is 3. To find the other coordinate point.

Q: If the lines 3x-4y+4=0 and 6x-8y-7=0 are tangents to a circle then find the radius of the circle.…

A: The diameter of circle is the perpendicular distance between the parallel lines (tangents) 3x-4y+4=0…

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find the distance from the poinst (-5, 2, -3) to the az-plane.

A: To find the distance from a point to the xz-plane, we are using the formula for the distance between…

Q: Let ∆ABC be a triangle. (a) Prove that B’ lies in the interior of AC if and only if ∠BAC and ∠ACB…

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Q: angle at whih the para bola intersects. the pesitive x-axis.

A: Angle of intersection means angle between tangent at intersection point with x axis. dy/dx =…

Q: Through any point (x, y) of a certain curve which passes through the origin. lines are dawn parallel…

A: Draw the sketch of two possible cases of the given problem:

Q: Segment AB has point A located at (6, 5). If the distance from A to B is 5 units, which of the…

A: The answer is given below:

Q: Find the locus of the midpoint of the chords of the circle x² + y² = a² which subtend a right angle…

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Q: 2. Through any point (x, y) of a certain curve which passes through the origin, lines are drawn…

A: We have given a point (x, y) of curve passes through (0,0), we need to find curve with given…

Q: Q10) Compute the length and the bearing of the perpendicular line that falling down from point R…

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Q: The midpoint of AB is at (-5, 3). If A = (4, -6), find В. B is:(

A: Mid point: If Ax1, y1 and Bx2, y2 are any two points then, the coordinates of the midpoint of AB are…

Q: Prove that the length of common chord of the two circles x + y² + 22x + c = (2² -c)(µ² +c) 2² + µ? O…

A: We will prove that the length of the common chord is the given term as following.

Q: If the distances from the origin of the centers of three circl x² + y² + 2A₁x − c = 0, (i = 1, 2,…

A: The centers of the given circles are (-λi,0),(i=1,2,3).The distances from the origin of the centers…

Q: Make a sketch of two parallel planes intersected by a third plane that is not parallel to the first…

A: To draw the sketch of two parallel planes intersected by a third plane that is not parallel to the…

Q: Consider the line segments (1,2) and (3,4). Prove that the lines are (i) non- collinear (ii)…

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Q: For Fano's geometry, prove that the lines through any one point of the geometry contain all the…

A: Given detail: For Fano's geometry, prove that the lines through any one point of the geometry…