Question

On a single set of axes, sketch a picture of the graphs of the following four equations: y = -x + V2. y = -x - v2, y = x + V2, and y = x-V2. These equations determine lines, which in turn bound a diemand Sheped region in the plane. (a) At how many points does the line y = -x + 2 intersect the unit circle? At how many points does the line y = -x-vī intersect the unit circle? At how many points does the line y=x+intersect the unit circle? 1 At how many points does the line y = x - intersect the unit circle? 1 1 (b) Find the intersection points between the unit circle and each of the four lines. (Order your answers from smallest to largest x, then from smallest to largest y.) Vai-VE) (x,y) - ha va V2 (X,Y)= (-) Viva (c) Construct a diamond shaped region in which the dircle of radius 1 centered at (-2,-5) sits tangentially. Use the techniques of this section to help. (Order your answers from smallest to largest slope, then from smallest to largesty Intercept. Use x as your variable.) y = -x+ 2 X y = (x+2) - V - 5 x y = -(x+2) - V2 X

Answer 1

Solution or Page 1 as st - rt 2 as 2 n+ 2 ne-2 u & unit circle cented at origen fy Graph 43-7+2 y = x+62 y=-1-52 to, (2) y=x-82 -2411201 2 n fo, f) we can see the above graph > All four lines intersect/ touch the unit circle at one point on only (b). Also, can find the co-ordinates of A, B, C & D Using mid point. DEL 1 - - -= =( A =( B = ( 1 / 2 we 1 J2 J2 - To J2 P. TO

Now, Part (c) Page 2 -5 -4 3 4 a 1t4 2 L2 T3 Li -2,-5) S Now, we have to find the equations of Li, L2, L3 of L4 At first, Equation of line L passing through the point R, Q f cenbe of circle o is given by Diamond 1 shape conspruct m (22-2,) = y +5=1(x+2) y = x-3 314-2+3 = 0 P.TO slope(m) y-y, -

Now, we Page 3 are. know that parallel L₃, Lu & L lines Also, distance betweeh Lz & i Ly & i Tunet - 1 unit 119 Apply distance (perpendicular) formula Ci-₂ P. fitme 3-c 1+12 =) 13-c] - 3-c с. Sz = + 2 3+2 & 3-52 G - 32 Ez = 3-2 Hence, Equation of L₂ y = x 3-52 C) y n Equation of Ly y = a-C2 =x-3 +52

Page 2 Similarly for lines L, & hz Equation of line paralel to Lif hz & passes through centre of circle is given by y +5 = -1 (+ 2) -> y = x - 7 = y + x + 7 =0 Applying perpendicular distance formula P = It m² -> 름 = 7 12 17-01 JE 72 tet (3=7+52 & 7- & Cu = 7-52 801 Equation of ti y=-x-C₃ y -7-7-72 Equation of hz y - x -C4 y = -x-7+52 -Answer THANK you

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