Mibvunzo Yemuenzaniso Kukurukura Kuenzana kweMutsetse weTangent kuDenderedzwa
Pendauluan
Kuenzanisa kwe tangent nedenderedzwa inyaya inokosha mukuongorora geometry. Kunzwisisa maitirwo ekuona equation ye tangent nedenderedzwa kunogona kubatsira kugadzirisa matambudziko akasiyana-siyana emasvomhu padanho repakati kusvika repamusoro. Chinyorwa chino chichakurukura mienzaniso yakasiyana-siyana yematambudziko uye nzira dzekuona equation ye tangent nedenderedzwa.
Tsanangudzo uye Dzidziso Yekutanga
Denderedzwa riri mu coordinate plane rinogona kumiririrwa ne quadratic equation:
\[ (x – a)^2 + (y – b)^2 = r^2 \]
apo \((a, b)\) ndiyo nzvimbo iri pakati pedenderedzwa uye \(r\) ndiyo nzvimbo iri pakati pedenderedzwa.
Mutsetse unobata denderedzwa kubva panzvimbo yekunze mutsetse unobata denderedzwa panzvimbo imwe chete chaiyo. Kana tikafunga kuti mutsetse une equation:
\[ y = mx + c \]
ipapo mamiriro ekuti mutsetse \(y = mx + c\) uchabatana nedenderedzwa anogona kuratidzwa nenzira inotevera:
\[ \sqrt{(a + bm)^2 – r^2} = |c| \]
Apo \(m\) iri gradient yemutsetse wetangent uye \(c\) iri constant.
Fomura yeEquation yeMutsetse weTangent
Kune tangent kudenderedzwa rine pakati \((0,0)\) uye radius \(r\), equation yaro panzvimbo \((x_1, y_1)\) padenderedzwa ndeiyi:
\[ x_1x + y_1y = r^2 \]
Asi kana pakati pedenderedzwa pari panzvimbo \((a, b)\), saka equation yacho ndeiyi:
\[ (x_1 – a)(x – a) + (y_1 – b)(y – b) = r^2 \]
Mibvunzo yemuenzaniso nehurukuro
Mubvunzo 1
Denderedzwa rine pakati pa \((3, 4)\) uye radius mayuniti mashanu. Tsvaga equation yemutsetse wetangent kubva pane poindi \((6, 8)\).
Kukurukurirana:
Mudambudziko iri, tinopiwa denderedzwa rine pakati pe \((3, 4)\), radius ye5, uye tinofanira kuwana equation yemutsetse wetangent kubva pane poindi \((6, 8)\). Heano matanho ekugadzirisa dambudziko iri:
1. Simbisa kuti poindi \((6, 8)\) haisi mukati medenderedzwa: \\
\[
\sqrt{(6-3)^2 + (8-4)^2} = \sqrt{3^2 + 4^2} = \sqrt{25} = 5
\]
Saka chinangwa chiri padenderedzwa kuitira kuti rigone kushandiswa kuwana mutsetse we tangent.
2. Kushandisa fomura:
\[
(x_1 – a)(x – a) + (y_1 – b)(y – b) = r^2
\]
\[
(6 – 3)(x – 3) + (8 – 4)(y – 4) = 5^2
\]
3. Nyoresa equation:
\[
3(x – 3) + 4(y – 4) = 25
\]
4. Kuvandudza:
\[
3x – 9 + 4y – 16 = 25
\]
\[
3x + 4y – 25 = 50
\]
Equation yemutsetse wetangent wakawanikwa ndeiyi:
\[
3x + 4y = 50
\]
Mubvunzo 2
Denderedzwa ne equation \[x^2 + y^2 = 16\]. Sarudza equation yemutsetse we tangent kubva pane poindi \((4, 0)\).
Kukurukurirana:
Denderedzwa rine pakati pa \((0, 0)\) uye radius ine mayuniti mana. Nzvimbo yekunze yakapihwa ndeye \((4, 0)\).
1. Kushandisa fomura yedenderedzwa rine pakati \((0, 0)\):
\[
x_1x + y_1y = r^2
\]
2. Kutsiva kukosha:
\[
4x + 0 \cdot y = 4^2
\]
3. Nyoresa:
\[
4x = 16
\]
\[
x = 4
\]
Zvinoreva kuti, tangent equation yatinayo ndeiyi:
\[
x = 4
\]
Mubvunzo 3
Chimiro chemutsetse unonamirana nedenderedzwa \((x+2)^2 + (y-3)^2 = 9\) panzvimbo \((-1, 5)\).
Kukurukurirana:
Denderedzwa rine pakati pa \((-2, 3)\) uye radius mayuniti matatu. Poindi ye tangency ndeye \((-1, 5)\).
1. Simbisa kuti pfungwa iri padenderedzwa:
\[
((-1+2)^2 + (5-3)^2) = 1 + 4 = 5 \neq 9 \rightarrow \text{not on the denderedzwa}
\]
Saka, panogona kunge paine chikanganiso mumhinduro yemubvunzo kana poindi. Kana \((-2, 6)\) yakapihwa sepoindi yekutarisa:
2. Nyoresa:
\[
(x_1-a)(xa) + (y_1-b)(yb) = r^2
\]
Kutsiva:
\[
(-2-(-2))(x+2) + (6-3)(y-3) = 9\]
Mhedzisiro:
\[
0 + 3(y-3) = 3^2
\]
\[
3y-9=9
\]
\[
y = 6
Zvinobuda kuti pfungwa iyoyo uye pfungwa:
y = 6 ichokwadi zvechokwadi.
Mhedziso tarisa musanganiswa, yeuka, nzira mbiri dzekuverenga.
inoshanda/nhema..Iyo Plus pfupiso gar. td 2; chimiro chinoshanda ne (grid). plis perimeter all coverage btns.
Ndatenda zvikuru uye ndinovimba izvi zvinobatsira shamwari dzangu.
Uyezve, dzidza pfungwa yekusimbisa kunzwisisa.
Avo vaisanzwisisa kare, kana Mwari achida, vachazopihwa matanho akadzama ekuvhiya akakosha.
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