Brief Course in Analytic Geometry |
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Common terms and phrases
a² b2 abscissa Analytic Geometry asymptotes Ax² bisectors bisects By² circle x² conic section conjugate hyperbola constant coördinate axes curve directrix ellipse equa equal EXERCISES find the coördinates Find the distance Find the equation Find the locus Find the points fixed point foci focus geometric given circle given equation given line given point hence hyperbola initial line latus rectum length line joining loci locus of equation m₁ middle point numbers origin P₂ parabola perpendicular point moves point of contact point P₁ point which moves points of intersection polar coördinates polar equation radical axis radius rectangular axes represents secant line secant method second degree Show sides slope standard equation standard form straight line subtangent tangent tangent and normal tion trace transformation triangle values variables vertex vertices Write the equations x-axis x₁ y-axis y-intercept y₁ y²+2 Gx
Popular passages
Page 194 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.
Page 84 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 144 - CON'IC, OR CONIC SECTION, n. Any curve which is the locus of a point which moves so that the ratio of its distance from a fixed point to its distance from a fixed line is constant.
Page 137 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 105 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 196 - Find the locus of a point the sum of whose distances from two given parallel lines is equal to a given length.
Page 153 - F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point...
Page 179 - To draw that diameter of a given circle which shall pass at a given distance from a given point. 9. Find the locus of the middle points of any system of parallel chords in a circle.
Page 114 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides. Show that the locus is a circle. 50. Prove that the two circles z2 + y2 + 2 G,z + 2 Ftf + Cj = 0 and x2 + y...
Page 57 - A point moves so that the difference of the squares of its distances from (3, 0) and (0, — 2) is always equal to 8.