7.3.5 Parallel and perpendicular lines
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205 214➤For the lines in RE7.3.4B determine:
(a) lines parallel to each of them through the origin,
(b) lines perpendicular to each of them through the point (−1, 1).7.3.6 Intersecting lines
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205 216
➤Find all points where the following lines intersect
(i) x+y= 1 (ii) 2x+ 2 y= 3 (iii) x−y= 17.3.7 Equation of a circle
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205 217➤A.Write down the equations of the circles with centres and radii:
(i) (−1, 1), 4 (ii) (2,−1), 1 (iii) (4, 1), 2B. Find the centre and radius of each of the circles:
(i) x^2 +y^2 − 2 x−y= 4 (ii) x^2 +y^2 + 3 x− 2 y− 7 = 0
(iii) x^2 +y^2 +y= 3C.A circle has the equationx^2 +y^2 − 4 y=0. Find its centre and radius, and the equation
of the tangents at the points (±
√
2 , 2 +√
2), using only geometry and trig. Also find
the point where the two tangents intersect.D.A circle has the equationx^2 +y^2 − 2 x=0. Determine its centre and radius, and find
the equation of the tangent at the point(
1
2,√
3
2). Determine where this tangent cuts
the axes.7.3.8 Parametric representation of curves
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205 219➤Eliminate the parameters in the following pairs of equations
(i) x=3cost, y=3sint
(ii) x= 1 +2cosθ, y= 3 −sinθ
(iii) x= 2 u^2 , y=u− 2(iv) x=2
t, y= 3 t(v) x=cos 2t, y=sint