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\(d\left(A,\left(\alpha\right)\right)=\frac{4}{3}\)
\(\left(\beta\right)\)//\(\left(\alpha\right)\) nên phương trình \(\left(\beta\right)\) có dạng : \(x+2y-2z+d=0,d\ne-1\)
\(d\left(A,\left(\alpha\right)\right)=d\left(A,\left(\beta\right)\right)\)\(\Leftrightarrow\frac{\left|5+d\right|}{3}=\frac{4}{3}\Leftrightarrow\begin{cases}d=-1\\d-9\end{cases}\)\(\Leftrightarrow d=-9\left(d=-1loai\right)\)\(\Rightarrow\left(\beta\right):x+2y-2z-9=0\)
a) a = c, b = – d b) a = – c, b = d
c) a = d, b = c d) a = – c, b = – d
Vậy \(S=4\pi r^2=4\pi\left(\dfrac{a\sqrt{2}}{2}\right)^2=2\pi a^2\) và \(V=\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\pi\left(\dfrac{a\sqrt{2}}{2}\right)^3=\dfrac{1}{3}\pi a^3\sqrt{2}\)
Ta có \(\overrightarrow{n}_{\beta}=\left(1;3k;-1\right);\overrightarrow{n}_{\gamma}=\left(k;-1;1\right)\)
Gọi \(d_k=\beta\cap\gamma\)
Gọi \(M\left(x;y;0\right)\) \(\Rightarrow OM^2=x^2+y^2\)
\(d^2\left(M;\left(\alpha\right)\right)=\frac{\left(x+2y+4\right)^2}{9}\) ; \(d^2\left(M;\left(\beta\right)\right)=\frac{\left(2x-2y-13\right)^2}{9}\)
\(\left(x+2y+4\right)^2=\left(2x-2y-13\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2y+4=2x-2y-13\\x+2y+4=-2x+2y+13\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4y+17\\3x=9\Rightarrow x=3\end{matrix}\right.\)
Th1: \(\left\{{}\begin{matrix}x=3\\x^2+y^2=\frac{\left(x+2y+4\right)^2}{9}\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3\\9y^2+81=4y^2+28y+49\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\5y^2-28y+32=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}M\left(3;4;0\right)\\M\left(3;\frac{8}{5};0\right)\end{matrix}\right.\)
TH2: \(\left\{{}\begin{matrix}x=4y+17\\x^2+y^2=\frac{\left(x+2y+4\right)^2}{9}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=4y+17\\\left(4y+17\right)^2+y^2=\left(2y+7\right)^2\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=4y+17\\13y^2+108y+240=0\end{matrix}\right.\) (vô nghiệm)
Bạn kiểm tra lại tính toán
a) α + β = 3 + 2i, α - β = 3 - 2i
b) α + β = 1 + 4i α - β = 1 - 8i
c) α + β = -2i, α - β = 12i
d) α + β = 19 - 2i α - β = 11 + 2i