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Find the the y-intercept of the line passing through A(2,3)=(h,k) which is perpendicular to the line through the points P(6,7)=(x1,y1) and Q(6,18)=(x2,y2).
slope of PQ = (y2-y1)/(x2-x1)=(18-7)/(7-6)=11
hence slope of its perpendicular = -1/11
eqn.of line through A is
y-k=m(x-h)
y-3=(-1/11)(x-2)= (-x/11) +(2/11)
y intercept is when x=0...we get
y-3 = 2/11
y=3+2/11=35/11
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specify the domain and range of the relation
x^2/18+(y-4)^2/4=1/2
(y-4)^2 = 4[0.5-x^2/18]=(4/18)[9-x^2]
since (y-4)^2 is always non -ve,9-x^2 shall be >=0
9>=x^2
3>=|x|
|x|<=3....is the domain..that is (-3,3)is the domain.
the function has a minimum at x=3....then y-4=0....y=4
hence range is [4,infinity)
